Showing papers in "Communications in Algebra in 1992"
TL;DR: In this paper, the prime radical of a module over a commutative ring is studied and discussed in the context of algebraic topology, and the authors show that it can be computed in polynomial time.
Abstract: (1992). On the prime radical of a module over a commutative ring. Communications in Algebra: Vol. 20, No. 12, pp. 3593-3602.
88 citations
TL;DR: In this article, Derivations et automorphismes de quelques algebras quantiques are derived from quantique automorphisms of quantique algebraic structures.
Abstract: (1992). Derivations et automorphismes de quelques algebras quantiques. Communications in Algebra: Vol. 20, No. 6, pp. 1787-1802.
88 citations
TL;DR: In this article, the authors use the theory of compressed algebras to construct forms F in five or more variables whose Gorenstein Artin algebra is not unimodal.
Abstract: A graded standard Gorenstein Artin algebra quotient of the polynomial ring R over k can be viewed as the algebra Af of partial differential operators of all degrees on a form F. The algebra A is unimodal if the Hilbert function has a single local maximum. We use the theory of compressed algebras to construct forms F in five or more variables whose Gorenstein algebras Af are not unimodal.
84 citations
TL;DR: In this paper, it was shown that the Ratliff-Rush ideal is the largest ideal for which, for sufficiently large positive integers n, (n) = I and hence that ̃̃ I = Ĩ.
Abstract: Ratliff and Rush show in particular that Ĩ is the largest ideal for which, for sufficiently large positive integers n, (Ĩ) = I and hence that ̃̃ I = Ĩ. We call regular ideals I for which I = Ĩ Ratliff–Rush ideals, and we call Ĩ the Ratliff–Rush ideal associated with I. It is easy to see that an element a of I : I is integral over I, in the sense that there is an equation of the form a + b1a k−1 + . . . + bk = 0, where bi ∈ I for i = 1, . . . , k. Therefore, the ideal Ĩ is always between I and the integral closure I ′ of I, and hence integrally closed ideals are Ratliff–Rush ideals. Ratliff and Rush observe [RR, (2.3.4)] that the powers of an invertible ideal are Ratliff–Rush ideals, so any principal ideal generated by a nonzerodivisor is a Ratliff–Rush ideal. They also prove the interesting fact that for any regular ideal I of R, there is a positive integer n such that for all k ≥ n, Ĩk = I [RR, (2.3.2)], i.e., all sufficiently high powers of a regular ideal are Ratliff–Rush. A regular ideal I is always a reduction of its associated Ratliff–Rush ideal Ĩ, in the sense that I(Ĩ) = (Ĩ) for some positive integer n. For the basic facts on reductions and reduction numbers of ideals, we refer the reader to [NR], [H1], and [H2]. In particular, if there is an element a of an ideal I for which aI = I then aR is called a principal reduction of I and the smallest n for which this equation holds is called the reduction number of I. We will call a regular ideal I stable iff it has a principal reduction with reduction number at most one, i.e., iff there is an element a of I for which
82 citations
81 citations
TL;DR: In this article, the fractional intersection and bivariant theory of fractional intersections are studied. But they do not consider the relation between the intersection and the bivariance.
Abstract: (1992). Fractional intersection and bivariant theory. Communications in Algebra: Vol. 20, No. 1, pp. 285-302.
76 citations
76 citations
TL;DR: The notion of hopf algebras over coideal subalgeses was introduced in this article, where the authors show that hopf algebra can be viewed as a hopf subalgebra.
Abstract: (1992). Freeness of hopf algebras over coideal subalgebras. Communications in Algebra: Vol. 20, No. 5, pp. 1353-1373.
62 citations
61 citations
TL;DR: Superalgebras J(F) of finite or infinite dimension obtained by the Kantor doubling process from dot-bracket superalges (F,., x ) with a supercommutative, associative product. and a superbracket x are examined.
Abstract: Superalgebras J(F) of finite or infinite dimension obtained by the Kantor doubling process from dot-bracket superalgebras (F, ., x ) with a supercommutative, associative product . and a superbracket x are examined. Such a superalgebra is Jordan if and only if x is a Jordan superbracket and is simple if and only if (F, ., x) is simple. Superalgebras J(F) of vector type where D is a derivation of (F, .)) are special. Superalgebras J(F) for poisson brackets F on even and odd variables are exceptional except in the case of a single odd variable and no even variables.
59 citations
TL;DR: In this paper, the authors investigated algebraic dependencies between skew derivations of a prime ring mainly in the case when they commute with basic automorphisms and considered a Hopf algebra defining by the skew derivation.
Abstract: In this paper we investigate algebraic dependencies between skew derivations of a prime ring mainly in the case when they commute with basic automorphisms; we also consider a Hopf algebra defining by the skew derivations and using its terms we discuss the problem about algebraic dependencies in general situation.
TL;DR: The main result of as discussed by the authors is equivalent to the following: if g is rigid then T is a maximal torus on n, and a classification of this law is given in the case in which the weights of T are kα, with 1≤k≤n=dimn.
Abstract: One knows that a solvable rigid Lie algebra is algebraic and can be written as a semidirect product of the form g=T⊕n if n is the maximal nilpotent ideal and T a torus on n . The main result of the paper is equivalent to the following: If g is rigid then T is a maximal torus on n . The authors then study algebras of this form where n is a filiform nilpotent algebra. A classification of this law is given in the case in which the weights of T are kα , with 1≤k≤n=dimn .
TL;DR: In this paper, the components of Hochschild homology in the case of strongly G graded algebra are described in terms of a spectral sequence where Hq (R,Sg ) is the Hochhedral homology of the identity component R = Se of S with coefficients in the bimodule Sg.
Abstract: Let be an algebra that is graded by a group G. Then the Hochschild and cyclic homologies of S have canonical decompositions with components labeled by the set T(G) of conjugacy classes of G : for Hochschild homology and similarly for cyclic homology. In this article, we describe the components of Hochschild homology in the case where S is strongly G graded.The description is given in terms of a spectral sequence where Hq (R,Sg ) is the Hochschild homology of the identity component R = Se of S with coefficients in the bimodule Sg and Hp (CG (g),.) is the group homology of the centralizer CG (g) of g in G. If R is a separable algebra then the spectral sequence degenerates and yields an isomorphism
TL;DR: In this paper, the indecomposable vector bundles are discussed and discussed in the context of algebraic vector bundling, and the authors propose a method to construct vector bundles.
Abstract: (1992). On indecomposable vector bundles. Communications in Algebra: Vol. 20, No. 5, pp. 1323-1351.
TL;DR: In this paper, the blocks of cyclic defect and green-orders are discussed and discussed in terms of green-order green-defects and cyclic defects, respectively.
Abstract: (1992). Blocks of cyclic defect and green-orders. Communications in Algebra: Vol. 20, No. 6, pp. 1715-1734.
TL;DR: In this paper, the authors describe Bezout and Prufer f-rings in terms of their localizations, and give a counter-example to show that the converse of the last assertion is false.
Abstract: This article describes Bezout and Prufer f-rings in terms of their localizations. All f-rings here are corrmutative, semi prime and possess an identity; they also have the bounded inversion property: a >1 implies that a is a multiplicative unit. The two main theorems are as follows: (1) A is a Bezout f-ring if and only if each localization at a maximal ideal is a (totally ordered) valuation ring; (2) Each Prufer f-ring is quasi-Bezout, and if each localization of A is a Prufer f-ring then so is A. We give a counter-example to show that the converse of the last assertion is false.
TL;DR: In this article, Centroids of nilpotent lie algabras are considered and centroids lie in a set of non-cooperative lie alga types.
Abstract: (1992). Centroids of nilpotent lie algabras. Communications in Algebra: Vol. 20, No. 12, pp. 3649-3682.
TL;DR: The notion of generalized inverses was introduced in this paper for continuous linear operators between Hilbert spaces and that of group inverse for elements of an associative algebra in any Jordan triple system (J, P).
Abstract: A notion of generalized inverse extending that of Moore—Penrose inverse for continuous linear operators between Hilbert spaces and that of group inverse for elements of an associative algebra is defined in any Jordan triple system (J, P). An element a∊J has a (unique) generalized inverse if and only if it is strongly regular, i.e., a∊P(a)2J. A Jordan triple system J is strongly regular if and only if it is von Neumann regular and has no nonzero nilpotent elements. Generalized inverses have properties similar to those of the invertible elements in unital Jordan algebras. With a suitable notion of strong associativity, for a strongly regular element a∊J with generalized inverse b the subtriple generated by {a, b} is strongly associative
TL;DR: In this article, the authors propose the generation of cleft comodule algabras using a cleft-commodule algebraic approach. But their work is limited.
Abstract: (1992). Genaralization fo cleft comodule algabras. Communications in Algebra: Vol. 20, No. 12, pp. 3703-3721.
TL;DR: An equiprime near-ring is a generalization of prime ring as mentioned in this paper, and its relation to the other notions of primeness for near-rings, primitive near-rings and near-fields is discussed.
Abstract: An equiprime near-ring is a generalization of prime ring. Firstly some axioma-tics concerning equiprime near-rings are discussed, e.g. their relation to the other notions of primeness for near-rings, primitive near-rings and near-fields. Secondly we investigate the equiprimeness of some well-known examples of near-rings.
TL;DR: In this paper, minimal overrings of a noetherian domain are discussed. But the authors focus on the minimal overheads of the noetherians and do not consider the non-overlapping domain.
Abstract: (1992). On minimal overrings of a noetherian domain. Communications in Algebra: Vol. 20, No. 6, pp. 1735-1746.
TL;DR: In this paper, it was shown that if k ≥ 1 is a positive integer, then D is a k-ha1f factorial domain (k-HFD) of order r>1 if the previous equality implies that s = t (mod r).
Abstract: Let D be a Dedekind domain. D is a half factorial domain (HFD) if for any irreducible elements of D the equality implies that s = t. D is a congruence half factorial domain (CHFD) of order r>1 if the same equality implies that s = t (mod r). In this paper we expand upon many of the known results for HFDs and CHFDs (see [6] and [7]) as well as introduce the following new class of domains: if k≥1 is a positive integer then D is a k—ha1f factorial domain (k—HFD) if s Skin the previous equality implies that s = t. In section I we explore the interrelationship of the HFD, CHFD, and k—HFD properties and offer a method for constructing examples of k—HFDs and CHFDs by viewing the class group of the given domain as a direct summand. In particular, we show in section I that the HFD, CHFD, and k—HFD properties are equivalent for rings of algebraic integers. In section II we extend the results of section I by constructing examples of Dedekind domains which are both CHFD and k—HFD but not HFD. In section In we explore...