Modules which are invariant under idempotents of their envelopes

Le Van Thuyet, Phan Dan, and Truong Cong Quynh. "Modules which are invariant under idempotents of their envelopes." Colloquium Mathematicae 143.2 (2016): 237-250. <http://eudml.org/doc/283540>.

@article{LeVanThuyet2016,
abstract = {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 $X = ⨁ _\{i∈ I\}X_\{i\}$, we have $M = ⨁ _\{i∈ I\} (u^\{-1\}(X_\{i\}) ∩ M)$. Moreover, some generalizations of -idempotent-invariant modules are considered.},
author = {Le Van Thuyet, Phan Dan, Truong Cong Quynh},
journal = {Colloquium Mathematicae},
keywords = {idempotent-invariant module; extending-invariant module; quasicontinuous},
language = {eng},
number = {2},
pages = {237-250},
title = {Modules which are invariant under idempotents of their envelopes},
url = {http://eudml.org/doc/283540},
volume = {143},
year = {2016},
}

TY - JOUR
AU - Le Van Thuyet
AU - Phan Dan
AU - Truong Cong Quynh
TI - Modules which are invariant under idempotents of their envelopes
JO - Colloquium Mathematicae
PY - 2016
VL - 143
IS - 2
SP - 237
EP - 250
AB - 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 $X = ⨁ _{i∈ I}X_{i}$, we have $M = ⨁ _{i∈ I} (u^{-1}(X_{i}) ∩ M)$. Moreover, some generalizations of -idempotent-invariant modules are considered.
LA - eng
KW - idempotent-invariant module; extending-invariant module; quasicontinuous
UR - http://eudml.org/doc/283540
ER -