Journal Article10.1080/00927872.2016.1243697
Simple-direct-modules
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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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Abstract: 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 Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M∕A≅B⊆⊕M and B simple, then A⊆⊕M In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject For example, we show that a ring R is uniserial (artinian serial) with J2(R) = 0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module)
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Citations
•Book
Classical artinian rings and related topics
TL;DR: A Theorem of Fuller Harada Rings The Structure Theory of Left Harada Ring Self-Duality of Left-Harada Ring Skew Matrix Ring The Structure of Nakayama Ring Modules over Nakaya Ring NakayAMA Algebras Local QF-rings as mentioned in this paper.
19
•Posted Content
On Simple-Direct Modules
TL;DR: In this article, the authors give a complete characterization of simple direct-projective modules over the ring of integers and over semilocal rings, and show that the rings whose simple-direct-injective right modules are projective are exactly the left perfect right $H$-rings.
4
On Simple-Direct Modules
TL;DR: In this article, simple direct-injective and direct-projective modules have been investigated in a series of papers, termed as simple-direct-injectionive and simple direct projective modules.
3
Artinian serial rings R with J3(R) = 0
Yasser Ibrahim,Yasser Ibrahim +1 more
TL;DR: In this article, the authors provided several new and interesting characterizations of artinian serial rings R with J3(R) = 0, which are nontrivial extensions of known results on the well-established cla...
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W. K. Nicholson,Mohamed Yousif +1 more
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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).
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