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On JB-Rings

Chinese Annals of Mathematics,Series B 2007年第6期28卷 617-628页

作者： huanyin chen Department of Mathematics Hunan Normal University Changsha 410006 China.

A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J（R）^2.

关键词： JB-Rings Exchange rings Subdirect product

Comparability for ideals of regular rings

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Science China Mathematics 2005年第6期48卷 757-768页

作者： chen huanyin Department of Mathematics Zhejiang Normal University Jinhua 321004 China

In this paper we investigate necessary and sufficient conditions under which the ideals possess comparability structure. For regular rings, we prove that every square matrix over ideals satisfying general comparabilit... 详细信息

关键词： comparability, QB-ideal, regular ring.

Strong Separativity over Regular Rings

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Algebra Colloquium 2015年第3期22卷 413-420页

作者： huanyin chen Department of Mathematics Hangzhou Normal University Hangzhou 310036 China

An ideal I of a ring R is strongly separative provided that for all finitely generated projective R-modules A, B with A = AI and B = BI, if 2A ≌ A ＋ B, then A ≌ B. We prove in this paper that a regular ideal I of a ring R is strongly separative if and only if each a E 1 ＋ I satisfying （1 - α）R ∝ r（a） is unit-regular, if and only if each a ∈ 1 ＋ I satisfying （1 - a2）R ∝ r（a2） is unit-regular, if and only if each a E 1 4- I satisfying R（1 - a）R = Rr（a） is unit-regular, if and only if each a ∈ 1 ＋ I satisfying R（1 -a^2）R = Rr（a^2） is unit-regular.

关键词： strongly separative ideal regular ideal annihilator

On Regular Power-Substitution

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 221-230页

作者： huanyin chen Department of Mathematics Hangzhou Normal University Hangzhou 310036 China

The necessary and sufficient conditions under which a ring satisfies regular power-substitution are investigated. It is shown that a ring R satisfies regular powersubstitution if and only if a-b in R implies that there exist n ∈ N and a U E GLn （R） such that aU = Ub if and only if for any regular x ∈ R there exist m,n ∈ N and U ∈ GLn（R） such that x^mIn = xmUx^m, where a-b means that there exists x,y, z∈ R such that a =ybx, b = xaz and x= xyx = xzx. It is proved that every directly finite simple ring satisfies regular power-substitution. Some applications for stably free R-modules are also obtained.

关键词： Regular power-substitution Regular power-cancellation Stably free module

Generalized Cline's Formula and Jacobson's Lemma in a Ring

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Algebra Colloquium 2024年第3期31卷 407-416页

作者： huanyin chen Marjan Sheibani School of Big Data Fuzhou University of International Studies and Trade Fuzhou 350202China Farzanegan Campus Semnan UniversitySemnanIran

We present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a *** generalized results extend many known results,e.g.,chen and Abdolyousefi[Generalized Jacobson's lemma in a Banach algebra,*** 49(2021)3263-3272],and Yan and Zeng[The generalized inverses of the products of two elements in a ring,Turkish ***.44(2020)1744-1756].

关键词： Cline's formula Jacobson's lemma generalized Drazin inverse Drazin inverse ring

Structure of Zhou Nil-clean Rings

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Algebra Colloquium 2018年第3期25卷 361-368页

作者： huanyin chen Marian Sheibani Department of Mathematics Hangzhou Normal University Hangzhou 311121 China Women's University of Semnan (Farzanegan) Semnan Iran

A ring R is Zhou nil-clean if every element in R is the sum of two tripotents and a nilpotent that commute. Homomorphic images of Zhou nil-clean rings are explored. We prove that a ring R is Zhou nil-clean if and only if 30 ∈ R is nilpotent and R/30R is Zhou nil-clean, if and only if R/BM（R） is 5-potent and BM（R） is nil, if and only if J（R） is nil and R/J（R） is isomorphic to a Boolean ring, a Yaqub ring, a Bell ring or a direct product of such rings. By means of homomorphic images, we completely determine when the generalized matrix ring is Zhou nil-clean. We prove that the generalized matrix ring Mn（R; s） is Zhou nil-clean if and only if R is Zhou nil-clean and s ∈ J（R）.

关键词： tripotent nilpotent homomorphic images generalized matrix rings Zhou nil-clean rings

SELF-CANCELLATION OF MODULES HAVING THE FINITE EXCHANGE PROPERTY

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Chinese Annals of Mathematics,Series B 2005年第1期26卷 111-118页

作者： chenhuanyin DepartmentofMathematics HunanNormalUniversityChangsha410006China

Self-cancellation of modules having the finite exchange property is introduced. If a right R-module M has the finite exchange property, it is shown that M has selfcancellation if and only if EndR(M) is a strongly sepa... 详细信息

关键词： Self-cancellation Strong separativity

A Note on Elements and Modules over Exchange Rings

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Communications in Mathematical Research 1999年第2期 115-119页

作者： chen huanyin (Department of Mathematics, Hunan Normal University, Changsha, 410006)

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ＬｅｔＲｂｅａｎａｓｓｏｃｉａｔｉｖｅｒｉｎｇｗｉｔｈｉｄｅｎｔｉｔｙ．ＡｒｉｇｈｔＲ－ｍｏｄｕｌｅＡｉｓｓａｉｄｔｏｓａｔｉｓｆｙｆｉｎｉｔｅｅｘｃｈａｎｇｅｐｒｏｐｅｒｔｙｉｆｆｏｒｅｖｅｒｙｒｉｇｈｔＲ－ｍｏｄｕｌｅＫａｎｄａｎｙｔｗｏｄｅｃｏ...

关键词： Exchange Ring Primitive Factor Weakly P exchange Ring

WHITEHEAD GROUPS OF MODULE EXTENSIONS

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Acta Mathematica Scientia 2004年第2期24卷 171-174页

作者：陈焕艮陈淼森 Zhejiang Normal Univ Dept Math Jinhua 321004 Peoples R China

When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings ... 详细信息

关键词： Whitehead group module extension (strong unit)1-stable range