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| Home > Articles > Published articles > Some characterizations of regular modules |
| Date: | 1990 |
| Abstract: | 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. |
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| Language: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Published in: | Publicacions matemàtiques, V. 34 n. 2 (1990) p. 241-248, ISSN 2014-4350 |
