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Weimin Xue (1996)
Publicacions Matemàtiques
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We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective covers are adapted from Azumaya’s generalized projective covers.
Goro Azumaya (1990)
Publicacions Matemàtiques
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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. ...
Gary Birkenmeier (1983)
Acta Universitatis Carolinae. Mathematica et Physica
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S. Balcerzyk (1971)
Colloquium Mathematicae
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Gerhard Racher (2010)
Banach Center Publications
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In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.
K. W. Roggenkamp (1970)
Compositio Mathematica
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Xiao Yan Yang, Zhong Kui Liu (2010)
Czechoslovak Mathematical Journal
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By analogy with the projective, injective and flat modules, in this paper we study some properties of -Gorenstein projective, injective and flat modules and discuss some connections between -Gorenstein injective and -Gorenstein flat modules. We also investigate some connections between -Gorenstein projective, injective and flat modules of change of rings.