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Some characterizations of regular modules
Azumaya, Goro

Data: 1990
Resum: Let M be a left modula over a ring R. M is called a Zelmanowitz-regular module if for each x Є M there exists a homomorphism f : M → R such that f(x)x = x . Let Q be a left R-module and h : Q → M a homomorphism . We call h locally split if for each x Є 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Publicat a: Publicacions matemàtiques, V. 34 n. 2 (1990) p. 241-248, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/37628
DOI: 10.5565/PUBLMAT_34290_02


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