Displaying similar documents to “On rings close to regular and p -injectivity”

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...

Diagonal reductions of matrices over exchange ideals

Huanyin Chen (2006)

Czechoslovak Mathematical Journal

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In this paper, we introduce related comparability for exchange ideals. Let I be an exchange ideal of a ring R . If I satisfies related comparability, then for any regular matrix A ∈ M n ( I ) , there exist left invertible U 1 , U 2 ∈ M n ( R ) and right invertible V 1 , V 2 ∈ M n ( R ) such that U 1 V 1 A U 2 V 2 = diag ( e 1 , ⋯ , e n ) for idempotents e 1 , ⋯ , e n ∈ I .

The maximal regular ideal of some commutative rings

Emad Abu Osba, Melvin Henriksen, Osama Alkam, Frank A. Smith (2006)

Commentationes Mathematicae Universitatis Carolinae

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In 1950 in volume 1 of Proc. Amer. Math. Soc., B. Brown and N. McCoy showed that every (not necessarily commutative) ring R has an ideal 𝔐 ( R ) consisting of elements a for which there is an x such that a x a = a , and maximal with respect to this property. Considering only the case when R is commutative and has an identity element, it is often not easy to determine when 𝔐 ( R ) is not just the zero ideal. We determine when this happens in a number of cases: Namely when at least one of a or 1 - a has a von...

VNR rings, Π -regular rings and annihilators

Roger Yue Chi Ming (2009)

Commentationes Mathematicae Universitatis Carolinae

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Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and Π -regular rings are studied. Properties of WGP-injectivity are developed.