منابع مشابه
Torsion-free Endotrivial Modules
Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We investigate the torsion-free part TF (G) of the group T (G) and look for generators of TF (G). We describe three methods for obtaining generators. Each of them only gives partial answers to the question but we obtain more p...
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There is a great deal of literature on periodic rings, respectively, torsion-free rings (especially of rank two). The aim of this paper is to provide a link between these two topics. All groups considered here are Abelian, with addition as the group operation. By order of an element we always mean the additive order of this element. All rings are associative but not necessarily with identity. T...
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Let R be a commutative ring with identity and let M be a torsion free R-module. Several characterizations of distributive modules are investigated. Indeed, among other equivalent conditions, we prove that M is distributive if and only if any primal submodule of M is irreducible, and, if and only if each submodule of M can be represented as an intersection of irreducible isolated components. MSC...
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We initiate the study of 1-torsion of finite modules over two-sided noetherian semiperfect rings. In particular, we give a criterion for determining when the 1-torsion submodule contains minimal generators of the module. We also provide an explicit construction for a projective cover of the submodule generated by the torsion elements in the top of the module. Some of the obtained results hold w...
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This paper defines an isomorphism, an anti-isomorphism and a Jordan isomorphism in a gamma ring and develops some important results relating to these concepts. Using these results we prove Herstein’s theorem of classical rings in case of prime gamma rings by showing that every Jordan isomorphism of a 2-torsion free prime gamma ring is either an isomorphism or an anti-isomorphism. AMS Mathematic...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1964
ISSN: 0021-8693
DOI: 10.1016/0021-8693(64)90023-7