Showing papers in "Communications in Algebra in 1975"
TL;DR: In this paper, the representation theory of artin algebras iii almost split sequences is studied and the authors propose a representation theory for almost-split sequences in algebraic graphs.
Abstract: (1975). Representation theory of artin algebras iii almost split sequences. Communications in Algebra: Vol. 3, No. 3, pp. 239-294.
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TL;DR: In this article, the authors present the Quasidirect products of quasigroups, which are the products of a quasigroup's quasiatic relation to a group.
Abstract: (1975). Quasidirect products of quasigroups. Communications in Algebra: Vol. 3, No. 9, pp. 835-850.
TL;DR: In this article, the weak local global principle in algebraic K-theory is investigated in various cases, including Witt and Grothendieck rings and their equivariant generalizations.
Abstract: Roughly speaking, the weak local global principle in algebraic K-theory assures that two locally isomorphic modules or forms differ- -on the level of Grothendieck rings - - by a nilpotent element only. This paper contains a thorough investigation of this rather useful principle in various cases, including Witt and Witt-Grothendieck rings and their equivariant generalizations. The proofs are based on an abstract categorical "localization lemma" which reduce s the proof in each special case to the verification of two simple assertions. In the .case of Witt rings the results are applied to deduce Pfister's basic structure theorems for Witt rings over arbitrary commutative rings from the corresponding statements for Witt rings over local rings. In the last section explicit isomorphisms of certain modules and forms, derived from locally isomorphic modules or forms in a canonical way, are exhibited. There are further possible applications of the results of this paper towards the theory of signatures of Witt rin...
TL;DR: In this paper, the authors cover space proofs in combinatorial group theory and show that space proofs for group theory can be used to prove the existence of groups in algebraic spaces.
Abstract: (1975). Covering space proofs in combinatorial group theory. Communications in Algebra: Vol. 3, No. 5, pp. 429-457.
TL;DR: A multivariate generalization of the Strong Liouville Theorem due to Risch is presented in this article, where a subfield of the field of complex numbers is considered.
Abstract: A multivariate generalization for line integrals of the Strong Liouville Theorem due to Risch is presented. The result is an abstract version of the following: Let k be a subfield of the field of complex numbers. Let each , be any function in a field E obtained by algebraic operations and the taking of logarithms and exponentials over . If there exists a functions g obtained by algebraic operations and the taking of logarithms and exponentials of elements of E such that then g must be of the form where do is in E, the ci are constants in k(a), and the di are elements in E(a), where a is a constant algebraic over E.
TL;DR: In this paper, Boolean orthogonalities and minimal prime ideals are studied in the context of algebraic geometry and algebraic algebraic programming. But they do not consider the problem of Boolean algebraic optimization.
Abstract: (1975). Boolean orthogonalities and minimal prime ideals. Communications in Algebra: Vol. 3, No. 10, pp. 859-900.
TL;DR: Adjoints to functors from categories of algebras were studied in this paper, where the functors are defined as a set of functors of the same type as the classes.
Abstract: (1975). Adjoints to functors from categories of algebras. Communications in Algebra: Vol. 3, No. 6, pp. 563-569.
TL;DR: In this article, an upper bound for the degree of the summands of a cyclic group of order 4 was derived, and it was shown that this bound is the exact value in all cases.
Abstract: Let G be the direct product of cyclic groups of order 4. we calculate an upper bound for the degree of the summands of gr ℤG. There are grounds for believing that this bound is, in fact, the exact value in all cases.
TL;DR: In this paper, the structure of splitting rings is studied and a discussion on splitting rings and splitting rings can be found in Section 3.3.1. Communications in Algebra: Vol. 3, No. 10, pp. 913-949
Abstract: (1975). On the structure of splitting rings. Communications in Algebra: Vol. 3, No. 10, pp. 913-949.
TL;DR: In this article, the authors present a model for finite groups with finite components in finite groups, where the components are defined by finite groups and finite groups are represented by finite components.
Abstract: (1975). 2-Components in finite groups. Communications in Algebra: Vol. 3, No. 10, pp. 901-911.