Journal ArticleDOI
Dual-square-free modules
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In this article, the class of dual-square-free (DSF) modules is defined, and the class is closed under direct summands and homomorphic images, and a modu...Abstract:
A module M is called dual-square-free (DSF) if M has no proper submodules A and B with M=A+B and M/A≅M/B. The class of DSF-modules is closed under direct summands and homomorphic images, and a modu...read more
Citations
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Journal ArticleDOI
Dual Utumi modules
Yasser Ibrahim,Mohamed Yousif +1 more
TL;DR: In this paper, a submodule N of a right R-module M is said to lie over a direct summand of M if, there is a decomposition M=M1⊕M2 with M 1⊆N and N ∩M 2,↪smallM2.
Journal ArticleDOI
Rings characterized by dual-Utumi-modules
TL;DR: In this article, a right R-module M is called dual-Utumi-module (DU-module) if for any two proper submodules A and B of M with M/A≅M/B and A + B = M, there exist summands K and L of M such that A = K ⊕ S1, B = L ⊆ S1.
Journal ArticleDOI
Rings whose injective hulls are dual square free
TL;DR: In this paper, the class of dual-square-free (DSF) modules is defined, and the class is closed under direct summands and homomorphic images, and a modu...
Journal ArticleDOI
U-Modules with transitive perspectivity
Yasser Ibrahim,Mohamed Yousif +1 more
TL;DR: In this paper, it was shown that if perspectivity is transitive in a Utumi-module M, then E(M) satisfies the substitution property and if M is either a quasi-continuous or an auto-invariant m...
References
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Book
Rings and Categories of Modules
Frank W. Anderson,Kent R. Fuller +1 more
TL;DR: In this paper, the authors provide a self-contained account of much of the theory of rings and modules, focusing on the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules.
Journal ArticleDOI
Lifting idempotents and exchange rings
TL;DR: In this article it was shown that a projective module P has the finite exchange property if and only if, whenever P = N + M where N and M are submodules, there is a decomposition P = A @ B with A S N and B C M.
Book
Continuous and Discrete Modules
Saad H. Mohamed,Bruno J. Müller +1 more
TL;DR: Continuous and discrete modules as discussed by the authors are generalizations of infective and projective modules respectively, and they provide an appropriate setting for decomposition theory of von Neumann algebras.
Journal ArticleDOI
Exchange rings and decompositions of modules
TL;DR: In this paper, a new class of rings, called exchange rings, is defined and studied, which includes regular rings in the sense of yon Neumann, local rings, and semiperfect rings, where the main property of these rings is that if a module has the finite exchange property (defined below) if and only if its endomorphism ring is an exchange ring, then any two direct sum decompositions of M have isomorphic refinements.
Journal ArticleDOI
Exchange rings, units and idempotents
Victor Camillo,Hua-Ping Yu +1 more
TL;DR: An associative ring R with identity is semiperfect if and only if every element of R is a sum of a unit and an idempotent, and R contains no infinite set of orthogonal idempotsents.