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Modules which are invariant under idempotents of their envelopes

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Thuyet L., Dan P., Quynh T.

Colloquium Mathematicum

2016

tom 143

nr 2

237-250

We study the class of modules which are invariant under idempotents of their envelopes. We say that a module M is 𝓧-idempotent-invariant if there exists an 𝓧-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 𝓧-idempotent-invariant if and only if for every decomposition $X = ⨁ _{i∈ I}X_{i}$, we have $M = ⨁ _{i∈ I} (u^{-1}(X_{i}) ∩ M)$. Moreover, some generalizations of 𝓧-idempotent-invariant modules are considered.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Dan P.

1 Quynh T.

1 Thuyet L.

1 2016

Wyniki wyszukiwania

Modules which are invariant under idempotents of their envelopes