Modules which are invariant under idempotents of their envelopes

• Autorzy: Le Van Thuyet , Phan Dan , Truong Cong Quynh
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16W20: Automorphisms and endomorphisms
• 16D50: Injective modules, self-injective rings
• 16D80: Other classes of modules and ideals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 2
• Strony: 237-250

Daty

wydano

2016

Twórcy

autor

Le Van Thuyet

• Department of Mathematics, Hue University, 3 Le Loi, Hue, Vietnam

autor

Phan Dan

• Banking University of Ho Chi Minh City, 39 Ham Nghi, Ho Chi Minh City, Vietnam

autor

Truong Cong Quynh

• Department of Mathematics, Danang University, 459 Ton Duc Thang, DaNang, Vietnam

Identyfikatory

DOI

10.4064/cm6496-1-2016