Generalized Stable Regular Rings

Chen, Huanyin

doi:10.1081/agb-120023138

Cited by 11 publications

(6 citation statements)

References 17 publications

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“…In [6], the author introduced a new class of rings, the generalized stable rings, so as to investigate directly infinite regular rings (cf. [7,8]). We say that a ring R is a generalized stable ring if aR + bR = R with a b ∈ R implies that there exist some s t ∈ R such that s a + by t = 1 for a y ∈ R. Many large classes of rings of interest are generalized stable rings.…”

Section: Introductionmentioning

confidence: 96%

On Generalized Stable Ideals

Chen

2010

Communications in Algebra

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An ideal I of a ring R is generalized stable in case aR + bR = R with a ∈ I b ∈ R implies that there exist s t ∈ 1 + I such that s a + by t = 1 for a y ∈ R. We establish, in this article, necessary and sufficient conditions for an ideal of a regular ring to be generalized stable. It is shown that every regular square matrix over such ideals admits a diagonal reduction. These extend the corresponding results of generalized stable regular rings.

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Section: Introductionmentioning

confidence: 96%

On Generalized Stable Ideals

Chen

2010

Communications in Algebra

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“…Furthermore, we prove that every regular matrix over a generalized stable exchange ring admits a diagonal reduction by quasi-invertible matrices. These give generalizations of [4,Theorem 2.4], [6,Theorem 16] and [7,Theorem 3].…”

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confidence: 99%

“…Also, we see that every element in a generalized stable regular ring is the product of an idempotent and two one-sided units (cf. [6,Lemma 14]). …”

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confidence: 99%

Generalized Stable Exchange Rings

Chen

2008

Algebra Colloq.

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A ring R is said to be a generalized stable ring provided that aR. If E is an exchange ring, then E is a generalized stable ring if and only if for any R-morphism f : A → M with Im f ≤ ⊕ M and any R-epimorphism g : A → M , there exist e = e 2 ∈ E and h ∈ K(E) such that f = g(eh). Furthermore, we prove that every regular matrix over a generalized stable exchange ring admits a diagonal reduction by quasi-invertible matrices.

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“…Di antaranya adalah Chen [2], Goodearl et al [5]. Keterkaitan antara ring reguler R dengan sifat ring stable range one dikemukakan oleh Chen [3]. Chen et al [4] memberikan bukti yang lain yang menunjukkan keterkaitan antara ring reguler yang memenuhi sifat stable range one dengan unit reguler.…”

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Relasi Ekuivalen Serupa Semu pada Ring Reguler Stable Diperumum

Yuliza

2016

jmi

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Dalam tulisan ini akan diselidiki relasi ekuivalen serupa semu pada ring reguler stable diperumum. Selanjutnya, akan diselidiki pula relasi ekuivalen serupa semu pada ring reguler stable diperumum dari himpunan bilangan bulat n. Awalnya, akan diselidiki relasi serupa semu bersifat refleksif pada ring reguler stable diperumum, relasi serupa semu bersifat simetris pada ring reguler stable diperumum dan relasi serupa semu bersifat transitif pada ring reguler stable diperumum. Kemudian, diselidiki relasi serupa semu bersifat refleksif pada ring reguler stable diperumum dari himpunan bilangan bulat n, relasi serupa semu bersifat simetris pada ring reguler stable diperumum dari himpunan bilangan bulat n dan relasi serupa semu bersifat transitif pada ring reguler stable diperumum dari himpunan bilangan bulat n.

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Generalized Stable Regular Rings

Cited by 11 publications

References 17 publications

On Generalized Stable Ideals

On Generalized Stable Ideals

Generalized Stable Exchange Rings

Relasi Ekuivalen Serupa Semu pada Ring Reguler Stable Diperumum

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