Showing papers in "Communications in Algebra in 1981"
TL;DR: In this paper, matched pairs of groups and bismash products of hopf algebras are used to construct hopf graphs. But they do not consider the relation between groups and groups.
Abstract: (1981). Matched pairs of groups and bismash products of hopf algebras. Communications in Algebra: Vol. 9, No. 8, pp. 841-882.
272 citations
TL;DR: In this article, generalized tilted algebras of type an are considered. But they are not considered in the context of algebraic geometry, and they do not have a fixed number of vertices.
Abstract: (1981). Generalized tilted algebras of type an. Communications in Algebra: Vol. 9, No. 20, pp. 2101-2125.
135 citations
TL;DR: In this paper it was shown that for two types of regular rings A ≥ 3 and n arbitrary, every element of A is a product of an element of (the group of elementary matrices) and a GLr(A) element.
Abstract: In this note we shall prove for two types of regular rings A that every element of is a product of an element of (the group of elementary matrices) and an element of GLr(A), for A ≥3 and n arbitrary. This is a kind of GLr-analogue of results of Lindel and Mohan-Kumar and is an extension of a result of Suslin.
72 citations
TL;DR: In this paper, a non-egenerate associative symmetric bilinear algebra with non-degenerate non-symmetric forms permitting composition is presented. But the authors do not specify the composition of the algebra.
Abstract: (1981). Algebras with nondegenerate associative symmetric bilinear forms permitting composition. Communications in Algebra: Vol. 9, No. 12, pp. 1233-1261.
54 citations
51 citations
50 citations
TL;DR: In this article, a right R-module X is called -injective provided each R-homomorphism ϕ: A → X with A in can be lifted to an R-Homomorphism θ: R→X.
Abstract: Let be a non-empty collection of right ideals of a ring R . A right R-module X is called -injective provided each R-homomorphism ϕ: A → X with A in can be lifted to an R-homomorphism θ: R→X . If R is a commutative Noetherian ring and . = Spec R then every -injective R-module is injective. On the other hand, if R is a commutative Noetherian integral domain of finite global dimension and a non-empty collection of prime ideals of R containing the zero ideal such that every -injective R-module is injective then = Spec R.
50 citations
TL;DR: In this paper, the abstract homomorphisms of algebraic groups are studied and problems and bibliographies are discussed. But the authors focus on the problem of finding a homomorphism of a group.
Abstract: (1981). Abstract homomorphisms of algebraic groups: problems and bibliography. Communications in Algebra: Vol. 9, No. 1, pp. 95-114.
39 citations
38 citations
37 citations
TL;DR: In this paper, the prime ideals in fixed rings were discussed. But they were not discussed in the context of algebraic geometry, and the authors focused on algebraic topology.
Abstract: (1981). Prime ideals in fixed rings. Communications in Algebra: Vol. 9, No. 4, pp. 423-449.
TL;DR: In this article, the degree of the dual of a grassman variety is defined as a degree of degree of duality of the grassman degree of a Grassman variety, i.e.,
Abstract: (1981). Degree of the dual of a grassman variety. Communications in Algebra: Vol. 9, No. 11, pp. 1215-1225.
TL;DR: The outer multiplicites of tensor product decompositions are computed for the smallest Euclidean Kac-Moody Lie algebra when one of the tensor factors is a fundamental module or the p-module as discussed by the authors.
Abstract: The outer multiplicites of tensor product decompositions are computed for the smallest Euclidean Kac-Moody Lie algebra when one of the tensor factors is a fundamental module or the p-module. Some combinatorial identities are obtained.
TL;DR: In this article, Coprimary decomposition, n-dimension and divtstbility are applied to artinian modules, where the n-dimensional dimension is defined as the number of vertices.
Abstract: (1981). Coprimary decomposition, n-dimension and divtstbility:Application to artinian modules. Communications in Algebra: Vol. 9, No. 11, pp. 1131-1146.
TL;DR: In this article, the projective line over a commutative ring with many units is shown to have Hua's Theorem and, from this, the Fundamental Theorem of Projective Geometry.
Abstract: This paper proves Hua's Theorem and, from this, the Fundamental Theorem of Projective Geometry for the projective line over a commutative ring with “many units”.
TL;DR: In this paper, the coordination of the Jordan triple system was discussed and discussed in the context of coordination in algebraic communication in algebras. But it was not discussed in detail.
Abstract: (1981). Coordinatization of jordan triple systems. Communications in Algebra: Vol. 9, No. 14, pp. 1495-1542.
TL;DR: In this article, the grade des modules sur certains anneaux filtres is presented, which is a grade based on the grade of annealing modules in algebraic programs.
Abstract: (1981). Grade des modules sur certains anneaux filtres. Communications in Algebra: Vol. 9, No. 15, pp. 1519-1532.
TL;DR: In this paper, the authors present an application for localement artiniennes in algebraic geometry, and apply it to a set of classes of artinienaux and modules.
Abstract: (1981). △-anneaux et modules △-injectifs. Applications aux categories localement artiniennes. Communications in Algebra: Vol. 9, No. 19, pp. 1981-1996.
TL;DR: In this article, the automorphisms of GL2(R) where R is a commutative ring having many units were examined and the results were shown to be equivalent to the results of this article when R is local ring having 2 a unit and residue class field.
Abstract: In this paper we examine the automorphisms of GL2(R) where R is a commutative ring having “many units” As a corollary we classify the automorphisms when R is a local ring having 2 a unit and residue class field not the field of 3 elements
TL;DR: In this paper, the authors studied the incidence algebra I (A, γ) of the category of paths in a (oriented multi-) graph γ over a ring A and gave necessary and sufficient conditions on γ and A in order to satisfy a polynomial identity, be prime, semi-prime, o r right Noetherian.
Abstract: In this paper, we study the incidence algebra I (A, γ) of the category of paths in a (oriented multi-) graph γ over a ring A.We describe relationships between algebraic properties of I(A, We describe relationships between algebraic properties of I(A, γ) and combinatorial features of γ. Specifically, we give necessary and sufficient conditions on γ and A in order that I(A, γ) satisfy a polynomial identity, be prime, semi-prime, o r right Noether-ian. We also determine the nil radical B (A, γ) of I(A, γ) for a large class of rings A, and show that under certain finiteness conditions, IiA, γ)/B (A, γ) i s isomorphic to the direct product of the incidence algebras of the strongly connected components of γ
TL;DR: In this article, Lie algebra associated with linear group is discussed. But the authors do not discuss the relation between linear groups and Lie Algebra with a linear group and linear groups.
Abstract: (1981). Lie algebra associated with linear group. Communications in Algebra: Vol. 9, No. 20, pp. 2075-2100.