Showing papers in "Communications in Algebra in 1980"
TL;DR: In this paper, a generator system of the ring of invariants of a finite reflection group is studied, and the generator system is shown to be a generator of a certain generator system for finite reflection groups.
Abstract: (1980). On a certain generator system of the ring of invariants of a finite reflection group. Communications in Algebra: Vol. 8, No. 4, pp. 373-408.
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TL;DR: In this paper, the structure of identity preserving functions which commute with every element of a set of automorphisms of a finite group G is investigated, where G is the set of elements of a group G of which A is an automorphism.
Abstract: Let A be a set of automorphisms of a finite group G. The structure of the near-ring C(A) of identity preserving functions which commute with every element of A is investigated.
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TL;DR: In this article, projective modules and their trace ideals are discussed and discussed in the context of projective algebra. But the authors do not discuss their relation to the present paper.
Abstract: (1980). Projective modules and their trace ideals. Communications in Algebra: Vol. 8, No. 19, pp. 1873-1901.
33 citations
TL;DR: In this paper, the generiators and normal subgroups of GL2(R) are described, where R is a commutative ring with "many units" and G is the number of units.
Abstract: This paper describes the generiators and normal subgroups of GL2(R) where R is a commutative ring with “many units”.
TL;DR: In this article, the authors introduce n-dimension and n-critical modules and apply them to artinian modules, where n is the number of elements in the n-dimensional space.
Abstract: (1980). N-dimension and n-critical modules.application to artinian modules. Communications in Algebra: Vol. 8, No. 16, pp. 1561-1592.
TL;DR: In this paper, the multilinear identities of the k×k matrices F2 were studied in terms of the cocharacters and codimension sequences, and the estimates were fairly good, while for k ≥ 3 only partial results were obtained.
Abstract: The multilinear identities of the k×k matrices F2 are studied in terms of the cocharacters and codimension sequences. For F2 the estimates are fairly good, while for k≥3 only partial results are obtained.
TL;DR: The divisor class group of a semigroup ring was studied in this article, where the authors propose a semidefinite version of the class group for semigroup rings.
Abstract: (1980). The divisor class group of a semigroup ring. Communications in Algebra: Vol. 8, No. 5, pp. 467-476.
TL;DR: In this paper, the relationship between certain classes of ideals in RH (or R) and the group ring RG is investigated by employing McCoy's "going up" and "going down" method.
Abstract: Let R be a ring with identity and H a normal subgroup of the group G. In this paper the relationship between certain classes of ideals in RH (or R) and the group ring RG is investigated by employing McCoy's “going up” and “going down” method which he used for polynomial rings in [2]. From the results obtained it is inferred that P(R)S = P(RS) if S is an u.p. - semigroup with unity, wher P(R) is the prime radical of R. If H is a central subgroup of G such that G/H is an u.p.- group, then P(RG) = P(RH)RG. Furthermore, if L(R) denotes the Levitzki nil radical of R, then it is proved that if R is any ring and S and ordered semigroup with unity, then L(RS) = L(R)S. Also, if G/H can be ordered then L(RH) ∗ RG = L(RG), while L(RH) = L(RG) ∩ RH for any central subgroup H of G. If the upper nil radical of R is denoted by U(R), and H is normal subgroup of G such that G/H can be ordered, then U(RG) ⊆ U(RH) ∗RG. If R is any ring and S an ordered semigroup with unity, then we have U(RS) ⊆ U(R)S.
TL;DR: In this article, the Picard group of a Grothendieck category has been studied in the context of algebraic geometry. But this work is limited to algebraic problems.
Abstract: (1980). On the Picard group of a Grothendieck category. Communications in Algebra: Vol. 8, No. 12, pp. 1169-1194.
TL;DR: In this article, the springer representations of chevalley groups op type f4 were studied and they were shown to have a similar behavior to the springers of Chevalley Group.
Abstract: (1980). On the springer representations of chevalley groups op type f4. Communications in Algebra: Vol. 8, No. 5, pp. 409-440.
TL;DR: In this paper, the Zeta functions of integral representations are used to represent integral representations in algebraic programs, and they are shown to be a function of integral representation of the zeta function.
Abstract: (1980). Zeta functions of integral representations. Communications in Algebra: Vol. 8, No. 10, pp. 911-925.
TL;DR: In this article, the socle of a ring is studied in terms of semisimple rings, and it is shown that a ring socle can be constructed from a ring's socle.
Abstract: (1980). On & - semisimple rings. A study of the socle of a ring. Communications in Algebra: Vol. 8, No. 10, pp. 889-909.
TL;DR: In this article, conditions on the commutative ring R and the semigroup ring S (with identity) are found which characterize those semigroup rings R[S] which are reduced or have weak global dimension at most one.
Abstract: In this paper conditions on the commutative ring R (with identity) and the commutative semigroup ring S (with identity) are found which characterize those semigroup rings R[S] which are reduced or have weak global dimension at most one. Likewise, those semigroup rings R[S] which are semihereditary are completely determined in terms of R and S.
TL;DR: In this article, it was shown that in an arbitrary alternative ring of characteristic ≠ 2, the fourth power of every associator is in the commutative center of the ring.
Abstract: Shestakov showed that in an arbitrary alternative ring of characteristic ≠ 2, the fourth power of every associator Is in the commutative center. He raised the question whether this might bp so for the square of every associator. The answer to this question is no, Which is demonsuapared by an exumple of an altor-native algobre of dimension 107.
TL;DR: In this article, it was shown that if G acts on R and if I is an essential right ideal of the fixed ring RG, then IR is essential in Rs. This result simplifies a number of proofs already in the literature.
Abstract: Let R ∗ G denote a crossed product of the finite group G over the ring R and let V be an R ∗ G-module. Maschke's theorem states that if 1/∣G∣ e R and if V is completely reducible as an R-module, then V is also completely reducible as an R ∗ G -module. In this paper, we obtain two applications of this theorem, both under the assumption that R is semiprime with no ∣G∣ -torsion. The first concerns group actions and here we show that if G acts on R and if I is an essential right ideal of the fixed ring RG , then IR is essential in Rs. This result, in turn, simplifies a number of proofs already in the literature. The second application here is a short proof of a theorem of Fisher and Montgomery which asserts that the crossed product R ∗ G is semiprime.