Open AccessJournal Article
Certain Rings Whose Simple Singular Modules Are nil-injective ∗
TL;DR: In this article, it was shown that if R is a left GMC2 left Goldie ring whose every simple singular left R -module is YJ-injective, then it is a finite product of a simple left MC2 ring.
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Abstract: In this paper, we first study some characterizations of left min-abel ring, strongly left min-abel ring and left MC2 ring. Next, we discuss and generalize some well known results for a ring whose simple singular left modules are nil- injective. Finally, as a byproduct of these results we are able to show that if R is a left GMC2 left Goldie ring whose every simple singular left R - module is YJ- injective, then R is a finite product of simple left Goldie ring.
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Citations
Quasi-Normal Rings
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•Journal Article
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TL;DR: In this paper, it was shown that a ring R is e-symmetric if and only if e is left semicentral and eRe is symmetric, where e is defined as a minimal idempotent.
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Some properties of e -symmetric rings
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TL;DR: In this paper, it was shown that R is an e-symmetric ring if and only if a 1a2a3 = 0 implies that aσ(1)aσ(2)a σ(3)e = 0, where σ is any transformation of {1, 2, 3}.
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Some Notes on Semiabelian Rings
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References
Rings with the dual of the isomorphism theorem
TL;DR: In this paper, it was shown that every left morphic ring is right principally injective, and use this to characterize the left perfect, right and left uniserial local rings.
93
Quasi-duo rings and stable range descent
Tsit Yuen Lam,Alex Dugas +1 more
TL;DR: In this article, the stable range of quasi-duo corner rings was studied and it was shown that for any semisplit corner ring R, the same is true for any semi-plit ring of R. This contrast with earlier results of Vaserstein and Warfield, which showed that the stable ranges can increase unboundedly upon descent to (even) Peirce corner rings.
73
Weakly continuous and c2-rings
W. K. Nicholson,Mohamed Yousif +1 more
TL;DR: A ring R is called right weakly continuous if the right annihilator of each element is essential in a summand of R, and R satisfies the right C2-condition.
49
Certain rings whose simple singular modules are GP-injective
Jin Yong Kim
- 01 Sep 2005
TL;DR: In this article, it was shown that a simple left Goldie ring with simple singular left $R$-modules are GP-injective is a finite product of simple left goldie rings.
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