# Some characterizations of regular modules.

Publicacions Matemàtiques (1990)

- Volume: 34, Issue: 2, page 241-248
- ISSN: 0214-1493

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topAzumaya, Goro. "Some characterizations of regular modules.." Publicacions Matemàtiques 34.2 (1990): 241-248. <http://eudml.org/doc/41129>.

@article{Azumaya1990,

abstract = {Let M be a left module over a ring R. M is called a Zelmanowitz-regular module if for each x ∈ M there exists a homomorphism F: M → R such that f(x) = x. Let Q be a left R-module and h: Q → M a homomorphism. We call h locally split if for every x ∈ M there exists a homomorphism g: M → Q such that h(g(x)) = x. M is called locally projective if every epimorphism onto M is locally split. We prove that the following conditions are equivalent:(1) M is Zelmanowitz-regular.(2) every homomorphism into M is locally split.(3) M is locally projective and every cyclic submodule of M is a direct summand of M.},

author = {Azumaya, Goro},

journal = {Publicacions Matemàtiques},

keywords = {Teoría de anillos; Anillos; Módulos; regular module; locally projective module; flat strict Mittag-Leffler module; locally split homomorphism; characterizations of regularity; left R-module; Zelmanowitz-regular; cyclic submodule; direct summand},

language = {eng},

number = {2},

pages = {241-248},

title = {Some characterizations of regular modules.},

url = {http://eudml.org/doc/41129},

volume = {34},

year = {1990},

}

TY - JOUR

AU - Azumaya, Goro

TI - Some characterizations of regular modules.

JO - Publicacions Matemàtiques

PY - 1990

VL - 34

IS - 2

SP - 241

EP - 248

AB - Let M be a left module over a ring R. M is called a Zelmanowitz-regular module if for each x ∈ M there exists a homomorphism F: M → R such that f(x) = x. Let Q be a left R-module and h: Q → M a homomorphism. We call h locally split if for every x ∈ M there exists a homomorphism g: M → Q such that h(g(x)) = x. M is called locally projective if every epimorphism onto M is locally split. We prove that the following conditions are equivalent:(1) M is Zelmanowitz-regular.(2) every homomorphism into M is locally split.(3) M is locally projective and every cyclic submodule of M is a direct summand of M.

LA - eng

KW - Teoría de anillos; Anillos; Módulos; regular module; locally projective module; flat strict Mittag-Leffler module; locally split homomorphism; characterizations of regularity; left R-module; Zelmanowitz-regular; cyclic submodule; direct summand

UR - http://eudml.org/doc/41129

ER -

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