Simple-direct-injective modules
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TL;DR: In this article, it was shown that a ring R is artinian serial with Jacobson radical square zero if and only if every simple-direct-injective right R-module is a C3-module.
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About: This article is published in Journal of Algebra. The article was published on 15 Dec 2014. and is currently open access. The article focuses on the topics: Simple module & Injective module.
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Citations
Simple-Direct-Projective Modules
TL;DR: In this article, the dual notion of simple-direct-injective modules was introduced and studied, and it was shown that a ring R is artinian and serial with J2(R) = 0 if and only if every simple direct-projective right R-module is quasi-Projective.
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Rings whose cyclics are C3-modules
TL;DR: In this article, a study of rings whose cyclic modules are D3-modules with applications to rings with cyclics are quasi-discrete and, respectively, discrete is presented.
10
T-continuous modules
TL;DR: In this article, it was shown that a module M is a t-continuous module if and only if M is t-extending and the endomorphism ring of M∕Z2(M) is von Neumann regular.
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Simple-direct-modules
TL;DR: A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with A≅B, and B⊆⊕M, then A⌆⌕M.
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Modules close to SSP- and SIP-modules
TL;DR: In this paper, it was shown that R is a semisimple artinian ring if and only if RR is SIP and every right R-module has a SIP-cover.
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References
•Book
Rings and Categories of Modules
Frank W. Anderson,Kent R. Fuller +1 more
- 01 Jan 1974
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.
3K
•Book
Continuous and Discrete Modules
Saad H. Mohamed,Bruno J. Müller +1 more
- 23 Feb 1990
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.
768
•Book
Quasi-Frobenius Rings
W. K. Nicholson,Mohamed Yousif +1 more
- 08 Sep 2003
TL;DR: A ring is called quasi-Frobenius if it is right or left selfinjective, and left or left artinian (all four combinations are equivalent).
Soc-Injective Rings and Modules*
TL;DR: In this paper, the notion of soc-injectivity was introduced and studied in the context of R-modules, where the socle of a semisimple submodule K of a submodule N is called Socle-Ninjective and any R-homomorphism f: K→M extends to N.
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