Showing papers in "Southeast Asian Bulletin of Mathematics in 2001"
TL;DR: In this paper, a complete classification for arc-transitive and one-regular Cayley graphs of valency at most four on finite abelian groups is given, and a classification of one regular Cayley graph is given.
Abstract: In this paper we give a complete classification for arc-transitive and one-regular Cayley graphs of valency at most four on finite abelian groups.
38 citations
TL;DR: In this article, a new type of elements of n-ary (n ≥ 3) semigroups with an idempotent identity was selected and properties of ideals connected with these elements were investigated.
Abstract: We select a new type of elements of n-ary (n ≥ 3) semigroups with an idempotent and investigate properties of ideals connected with these elements.
37 citations
TL;DR: In this article, a convolution operator on Σp is introduced, and sharp inequalities for f(z) ∈ Σ satisfying Re{(1 − α)z� p�� p� (a + 1, c) f(p) > β, where α ≥ 0, β 0 and c ≠ 0, − 1, − 2, −2, etc.
Abstract: Let Σ (p ∈ N) be the class of functions $$f(z) = z^{-p} + \sum^{\infty}_{n = 1} a_{n-p} z^{n-p}$$
analytic in 0 < |z| < 1. A convolution operator L
p
(a, c) on Σp is introduced. This paper gives some sharp inequalities for f(z) ∈ Σ satisfying Re{(1 − α)z
p
L
p
(a, c) f(z) + αz
p
L
p
(a + 1, c) f(z)} > β, where α ≥ 0, β 0 and c ≠ 0, −1, −2,....
29 citations
TL;DR: In this article, the authors classify the indecomposable secondary modules over local dedekind domains and establish a connection between them and pure-injective modules over such domains.
Abstract: The aim of this paper is to classify the indecomposable secondary modules over local dedekind domains and to establish a connection between the indecomposable secondary modules and the indecomposable pure-injective modules over such domains.
17 citations
TL;DR: In this paper, the authors considered the Differential Equation of the form ty(n)(t) + my(n−1) + ty(t) = 0 (1) where m is any integer and n ≥ 2 for t ∈ (−∞, ∞).
Abstract: Consider the Differential Equation of the form ty(n)(t) + my(n−1)(t) + ty(t) = 0 (1) where m is any integer and n ≥ 2 for t ∈ (−∞, ∞). It is found that the values of m make the solutions of (1) to be classical, that is the solutions in the space C(−∞, ∞) of continuous functions, or the Distributions which are the solutions in the space D’
R
of Distributions whose supports are bounded on the left.
11 citations
TL;DR: In this paper, the authors unify and extend results which characterise when certain transformation semigroups defined on a set are (locally) factorisable, and consider the corresponding problem for the semigroup of linear transformations of a vector space.
Abstract: A semigroup S is factorisable if S = GE = EG where G is a subgroup of S and E is the set of idempotents in S; and S is locally factorisable if eSe is factorisable for every e ∈ E. In this paper, we unify and extend results which characterise when certain transformation semigroups defined on a set are (locally) factorisable, and we consider the corresponding problem for the semigroup of linear transformations of a vector space.
11 citations
TL;DR: In this article, some aspects of polygroups are introduced Semi-direct hyperproduct of two polygroups is defined and the concept of weak polygroups and a generalization of Cayley's theorem for permutation weak poly groups is obtained.
Abstract: In this paper, some aspects of polygroups are introduced Semi-direct hyperproduct of two polygroups is defined We also introduce the concept of weak polygroups and obtain a generalization of Cayley’s theorem for permutation weak polygroups
10 citations
TL;DR: In this article, three logarithmic operators in the ring of arithmetic functions, namely those of Rearick, Carlitz-Subbarao and Shapiro, are considered and characterizations of completely multiplicative functions are derived as application.
Abstract: Three logarithmic operators in the ring of arithmetic functions, namely those of Rearick, Carlitz-Subbarao and Shapiro, are considered. Apart from the distinction of values at n = 1, all three logarithms are proved to be essentially the same. Some characterizations of completely multiplicative functions are derived as application.
10 citations
TL;DR: A new family of numerical methods of arbitrarily high order for systems of first-order differential equations which are to be termed pseudo two-step Runge-Kutta methods are designed by using collocation techniques.
Abstract: The aim of this paper is to design a new family of numerical methods of arbitrarily high order for systems of first-order differential equations which are to be termed pseudo two-step Runge-Kutta methods. By using collocation techniques, we can obtain an arbitrarily high-order stable pseudo two-step Runge-Kutta method with any desired number of implicit stages in retaining the two-step nature. In very first investigations, the pseudo two-step Runge-Kutta methods are shown to be promising numerical integration methods.
7 citations
TL;DR: In this paper, the endomorphism spectrum and endomorphisms of bipartite graphs with diameter three and girth six are defined and a more systematic treatment of these endomorphivities is given.
Abstract: There are different endomorphisms for a graph. For a more systematic treatment of these endomorphisms the endomorphism spectrum and the endomorphism type of a graph are defined. Knauer characterized trees using their endomorphism types. The endomorphism type of bipartite graphs with diameter three and girth six is given in this paper.
6 citations
Journal Article•
TL;DR: In this article, it was shown that for any positive integer n, the multiplicative semigroup Z n has the property that the set of bi-and quasi-ideals coincide if and only if either n = 4 or n is square-free.
Abstract: We show that for any positive integer n, the multiplicative semigroup Z n has the property that the set of bi-ideals and the set of quasi-ideals coincide if and only if either n = 4 or n is square-free.
TL;DR: In this article, the Fourier-Mukai transform is extended to the context of Higgs bundles under certain conditions and some results valid for sheaves on abelian varieties and K3 surfaces are extended for the situation of higgs bundles.
Abstract: The Fourier-Mukai transform is extended to the context of Higgs bundles under certain conditions Some results valid for sheaves on abelian varieties and K3 surfaces are extended to the situation of Higgs bundles An application to the relative setting is given
TL;DR: The history of algebra is reviewed in order to outline its present state and the reader is urged to focus attention to the need for algebraic considerations in all parts of mathematics but also outside of mathematics.
Abstract: At the turn of the century it seems to be appropriate to pause and to try to envision future possibilities. We want to discuss the prospects of algebra. To look into the future requires an understanding of the past, the longstanding aims, but also the difficulties which have been encountered. We are going to review part of the history of algebra in order to outline its present state. It is important to notice the missed opportunities and to analyze the reasons. To recognize the present possibilities requires to be aware of the tools which now are available and which may not yet have been used in an optimal way. We urge the reader to focus attention to the need for algebraic considerations in all parts of mathematics but also outside of mathematics. Of course, a view back should also strengthen the interest in classical open problems which now may be feasible to attack.
TL;DR: In this paper, a continuation work of the author's on μ(z)-homeomorphisms is presented, where the authors establish similar relationships between quasisymmetric function and dilatation function as in quasiconformal mappings under µ(z) homeomorphisms.
Abstract: This paper is a continuation work of the author’s on μ(z)-homeomorphisms. We establish similar relationships between quasisymmetric function and dilatation function as in quasiconformal mappings under μ(z)-homeomorphisms. Furthermore, a weighted quasiisometric inequality is presented.
TL;DR: In this paper, a complete classification of the regular p-groups with e-invariants (e, 2, 1) is given, using the algorithms for determining the isomorphic regular P-groups.
Abstract: The class of the regular p-groups is one of the important classes in p-groups. Not only it has many similar properties as abelian p-groups, but also many of the p-groups belong to this class. In this paper, using the algorithms for determining the isomorphic regular p-groups, we give a complete classification of the regular p-groups with e-invariants (e, 2, 1).
TL;DR: In this paper, it was shown that if rings A and B are s;2-rings, then so is the ring of aMorita context, and analogous results for unit 1-stable ranges and GM-rings.
Abstract: Department of Mathematics, Hunan Normal University, Changsha 410006, P.R. ChinaE-mail: chyzxl@sparc2.hunnu.edu.cn2000 Mathematics Subject Classification: 16U99, 16E50Abstract. In this paper, we show that if rings A and B are –s;2ƒ-rings, then so is the ring of aMorita context –A;B;M;N;c;fƒ. Also we get analogous results for unit 1-stable rangesand GM-rings. These give new classes of rings satisfying such stable range conditions.Keywords: Morita context, unit 1-stable range, GM-ring
TL;DR: In this article, the authors considered the class of analytic and univlent functions with negative coefficients and with fixed second coefficient, and derived the coefficients for f(z) in the class L petertodd c istg *(α,β,γ) consisting of analytic functions with positive coefficients and fixed second coefficients.
Abstract: In this paper we consider the class L
c
*(α,β,γ) consisting of analytic and univlent functions with negative coefficients and with fixed second coefficient. The object of the present paper is to show coefficient estimates, convex linear combinations, some distortion theoems and radii of starlikeness and convexity for f(z) in the class L
c
*(α,β,γ). The results are generalized to families with finitely many fixed coefficients.
TL;DR: In a regular semigroup S, an inverse subsemigroup S of S is called an inverse transversal of S if S° contains a unique inverse x° of each element x of S.
Abstract: In a regular semigroup S, an inverse subsemigroup S° of S is called an inverse transversal of S if S° contains a unique inverse x° of each element x of S. An inverse transversal S° of S is called a Q-inverse transversal of S if S° is a quasi-ideal of S.
TL;DR: In this article, the Fischer matrices for the conjugacy classes of the affine group H petertodd n� (q) for arbitrary n = 2, 3, 4 and the number of irreducible characters of H2, H3, and H4 were obtained.
Abstract: Let GL
n
(q) be the general linear group and let H
n
; V
n
(q) · GL
n
(q) denote the affine group of V
n
(q). In [1] and [4], we determined Fischer matrices for the conjugacy classes of GL
n
(q) where n = 2, 3, 4 and we obtained the number of conjugacy classes and irreducible characters of H2, H3, and H4. In this paper, we find the Fischer matrices of the affine group H
n
for arbitrary n.
TL;DR: In this article, the general upper bounds for the second order dehn functions of split extensions of split extension have been established, and a general upper bound for split extensions has been given.
Abstract: In this paper, we set up the general upper bounds for the second order dehn functions of split extensions.
TL;DR: In this paper, it was shown that for any positive integer k > 1, the largest prime divisor P(k) ≥ 2m+2(4m + 9) + 1 for all m ≥ 4.
Abstract: For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if F
m
= 22m + 1 is the m‘th Fermat number, then P(F
m
) ≥ 2m+2(4m + 9) + 1 for all m ≥ 4. We also give a lower bound of a similar type for P(F
a,m
), where F
a,m
= a2m + 1 whenever a is even and m ≥ a18.
TL;DR: In this article, generalized s-comparability over regular rings is investigated and generalized results for regular rings satisfying general comparability are given. But they also give generalizations of the corresponding results over non-regular rings.
Abstract: In this paper, we investigate generalized s-comparability over regular rings. These also give generalizations of the corresponding results over regular rings satisfying general comparability.
TL;DR: In this paper, a generalized Witt algebra and a Hamiltonian algebra were constructed by using additive maps, where 1 ≤ p ≤ n from a set of integers into a field of characteristic zero.
Abstract: We construct a generalized Witt algebra W(g
p
, h
p
, n) and a Hamiltonian algebra $$ \overline{H(g_{2n}, h_{2n}, 2n}$$
by using additive maps g
p
, h
p
where 1 ≤ p ≤ n from a set of integers into a field of characteristic zero. We show that the Lie algebras W(g
p
, h
p
, n). and $$ \overline{H(g_{2n}, h_{2n}, 2n} $$
are simple if g
p
and h
p
are injective, and also that the Lie algebras W(g
p
, h
p
, n) and $$ \overline{H(g_{2n}, h_{2n}, 2n} $$
have no ad-diagonal elements with respect to the standard basis.
TL;DR: In this article, a condition in form of a polynomial for the existence of groups Δ (2, 3, k) as subgroups of PSL(2, q) or PGL(2. q) was given.
Abstract: In this paper we are interested in triangle groups Δ (j, k, l) where j = 2 and k = 3. The groups Δ (j, k, l) can be considered as factor groups of the modular group PSL(2, Z) which has the presentation 〈x, y : x2 = y3 = 1〉. Since PSL(2,q) is a factor group of Gk,l,m if -1 is a quadratic residue in the finite field Fq, it is therefore worthwhile to look at Δ(j, k, l) groups as subgroups of PSL(2, q) or PGL(2, q). Specifically, we shall find a condition in form of a polynomial for the existence of groups Δ (2, 3, k) as subgroups of PSL(2, q) or PGL(2, q).
TL;DR: In this paper, it was shown that if R is a Min-E ring, then the following statements are equivalent: (1) every left primitive factor ring of R is left artinian; (2) R is π-regular ring; (3) r is an exchange ring; and (4) r r is a Clean ring.
Abstract: In this paper, we prove that if R is a Min-E ring, then the following statements are equivalent: (1) Every left primitive factor ring of R is left artinian; (2) R is a π-regular ring; (3) R is an Exchange ring; (4) R is a Clean ring. As an application, we obtain that if R is Min-E ring, every left primitive factor ring of R is artinian and any direct product of them is a Min-E ring, then every non-zero homomorphic image of R contains only a finite number of prime ideals. When R is Min-E ring and has no infinite set of orthogonal idempotents, a left R-module M is Min-E if and only if M is Max-E. Also, we show, if R is a strongly clean Min-E ring, then R is directly finite and has stable range 1.
TL;DR: In this article, the generalized bicyclic semigroups are considered and the word problem for these kinds of semigroup is solved. But the problem is not solved for the Jones semigroup and the semigroup C = 〈a, b | a2b = a, ab2 = b〉.
Abstract: In this paper, we consider the generalized bicyclic semigroups B
n
= 〈a, b | a
n
b = 1〉 and the Jones semigroups A
n
= 〈a, b | an+1b = a〉. They are the generalizations of the bicyclic semigroup B = 〈a, b | ab = 1〉 and its analogous semigroup A = 〈a, b | a
2
b = a〉 discovered by P.R., Jones in 1987. The word problem for these kinds of semigroups is solved. It is proved that, for n ≥ 2, B
n
are bisimple right inverse but not inverse semigroups and that the semigroup C = 〈a, b | a2b = a, ab2 = b〉 is the smallest idempotent-free homomorphic image of A
n
. Moreover, we also prove that A
n
and A
m
are mutually embeddable but not isomorphic with each other if n ≠ m. As a consequence, different kind of $${\cal D}$$
-nontrivial [0-]simple semigroups without idempotents are discussed.
TL;DR: In this article, it was shown that weakly π'-Engel conditions are closely related to the existence of normal π-complements, and that π´-Engels conditions are related to π -nilpotent groups.
Abstract: In this paper we show that the weakly π’-Engel conditions are closely related to the existance of normal π-complements; while the π’-Engel conditions are closely related to the π-nilpotent groups.
TL;DR: In this article, the finite exchange property of modules with finite exchange has been studied and the answer is affirmative for module M with infinite exchange property, i.e., M = ⊕{Mi | i ∈ I} and N a summand of M.
Abstract: The purpose of this paper is to answer an open problem proposed by Matlis on modules with the finite exchange property. The problem is: Let {Mi | i ∈ I} be an indexed family of indecomposable injective modules and M a direct sum of Mi, i.e. M = ⊕{Mi | i ∈ I} and N a summand of M. Is N a direct sum of indecomposable injective modules, i.e. N = ⊕{Mj|j ∈ J, J ⊂ I}? The answer to this problem is affirmative for module M with finite exchange property.