منابع مشابه
Projective Summands in Generators
An i?-module Mis a generator (of the category of modules) provided every module is a homomorphic image of a suitable direct sum of copies of M. Equivalently, some M has R as a summand. Except in the last section, all rings are assumed to be commutative, Noetherian domains, and modules are usually finitely generated. In this context generators are exactly those modules that have non-zero free su...
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Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R is Gorenstein if and only if some syzygy module of k has a G-projective summand.
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The aim of this paper is to prove a general version of Plünnecke’s inequality. Namely, assume that for finite sets A, B1, . . . Bk we have information on the size of the sumsets A + Bi1 + · · · + Bil for all choices of indices i1, . . . il. Then we prove the existence of a non-empty subset X of A such that we have ‘good control’ over the size of the sumset X + B1 + · · · + Bk. As an application...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1982
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000019851