منابع مشابه
Decompositions of Reflexive Modules
In a recent paper [11] we answered to the negative a question raised in the book by Eklof and Mekler [8, p. 455, Problem 12] under the set theoretical hypothesis of ♦א1 which holds in many models of set theory. The Problem 12 in [8] reads as follows: If A is a dual (abelian) group of infinite rank, is A ∼= A⊕Z? The set theoretic hypothesis we made is the axiom ♦א1 which holds in particular in G...
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Article history: Received 23 August 2012 Available online xxxx Communicated by Luchezar L. Avramov MSC: 16G50 13B02 16E65
متن کاملDecompositions of Modules and Comodules
It is well-known that any semiperfect A ring has a decomposition as a direct sum (product) of indecomposable subrings A = A1 ⊕ · · · ⊕ An such that the Ai-Mod are indecomposable module categories. Similarly any coalgebra C over a field can be written as a direct sum of indecomposable subcoalgebras C = ⊕ I Ci such that the categories of Ci-comodules are indecomposable. In this paper a decomposit...
متن کاملA Note on Cancellation of Reflexive Modules
By the Quillen-Suslin theorem [Qui76, Sus76], we know that projective modules over a polynomial ring over a field are free. One way of saying this is, that if two projective modules of the same rank are stably isomorphic, then they are isomorphic. That, projective modules of given rank over polynomial rings are stably isomorphic was well known at the time Quillen and Suslin proved their theorem...
متن کاملResolving Decompositions for Polynomial Modules
We introduce the novel concept of a resolving decomposition of a polynomial module as a combinatorial structure that allows for the effective construction of free resolutions. It provides a unifying framework for recent results of the authors for different types of bases.
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2001
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s000130050557