Modules which are invariant under idempotents of their envelopes
Le Van Thuyet ; Phan Dan ; Truong Cong Quynh
Colloquium Mathematicae, Tome 144 (2016), p. 237-250 / Harvested from The Polish Digital Mathematics Library
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We study the class of modules which are invariant under idempotents of their envelopes. We say that a module M is -idempotent-invariant if there exists an -envelope u : M → X such that for any idempotent g ∈ End(X) there exists an endomorphism f : M → M such that uf = gu. The properties of this class of modules are discussed. We prove that M is -idempotent-invariant if and only if for every decomposition X=⨁i∈IXi, we have M=⨁i∈I(u-1(Xi)∩M). Moreover, some generalizations of -idempotent-invariant modules are considered.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:283540 
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Le Van Thuyet; Phan Dan; Truong Cong Quynh. Modules which are invariant under idempotents of their envelopes. Colloquium Mathematicae, Tome 144 (2016) pp. 237-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6496-1-2016/