Displaying similar documents to “Quasiregular rings”

New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith (1996)

Publicacions Matemàtiques

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A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.

Solutions of minus partial ordering equations over von Neumann regular rings

Yu Guan, Zhaojia Tong (2015)

Open Mathematics

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In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.

On p -injectivity, YJ-injectivity and quasi-Frobeniusean rings

Roger Yue Chi Ming (2002)

Commentationes Mathematicae Universitatis Carolinae

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A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms...

On non singular p-inyective rings.

Yasuyuki Hirano (1994)

Publicacions Matemàtiques

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A ring R is said to be if, for any principal left ideal I of R, any left R-homomorphism I into R extends to one of R into itself. In this note left nonsingular left p-injective rings are characterized using their maximal left rings of quotients and the structure of semiprime left p-injective rings of bounded index is investigated.