EuDML | Browse

Let $R$ be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in $R$ is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.

Exchange rings satisfying the related comparability.

Huanyin Chen, Fu-An Li (2002)

Collectanea Mathematica

In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.

Exchange rings with stable range one

Huanyin Chen (2007)

Czechoslovak Mathematical Journal

We characterize exchange rings having stable range one. An exchange ring $R$ has stable range one if and only if for any regular $a \in R$ , there exist an $e \in E (R)$ and a $u \in U (R)$ such that $a = e + u$ and $a R \cap e R = 0$ if and only if for any regular $a \in R$ , there exist $e \in r . a n n (a^{+})$ and $u \in U (R)$ such that $a = e + u$ if and only if for any $a, b \in R$ , $R / a R ≅ R / b R ⟹ a R ≅ b R$ .

Ext and von Neumann regular rings

Jan Trlifaj (1985)

Czechoslovak Mathematical Journal

Extensions of $G M$ -rings

Huanyin Chen, Miaosen Chen (2005)

Czechoslovak Mathematical Journal

It is shown that a ring $R$ is a $G M$ -ring if and only if there exists a complete orthogonal set ${e_{1}, \dots, e_{n}}$ of idempotents such that all $e_{i} R e_{i}$ are $G M$ -rings. We also investigate $G M$ -rings for Morita contexts, module extensions and power series rings.

Finitely generated projective ideals in commutative rings.

B. William Irlbeck (1978)

Journal für die reine und angewandte Mathematik

Fully idempotent near-rings and sheaf representations.

Ahsan, Javed, Mason, Gordon (1998)

International Journal of Mathematics and Mathematical Sciences

Generalized adjoint semigroups of a ring.

Du, Xiankun, Wang, Junlin (2006)

Beiträge zur Algebra und Geometrie

Generalized SV-modules.

Abyzov, A.N. (2009)

Sibirskij Matematicheskij Zhurnal

Generalized $V$ -rings and von Neumann regular rings

Giuseppe Baccella (1984)

Rendiconti del Seminario Matematico della Università di Padova

Generalized V-Rings.

K.M. Rangaswamy, V.S. Ramamurthi (1972)

Mathematica Scandinavica

Generators of existence varieties of regular rings and complemented Arguesian lattices

Christian Herrmann, Marina Semenova (2010)

Open Mathematics

We proved in an earlier work that any existence variety of regular algebras is generated by its simple unital Artinian members, while any existence variety of Arguesian sectionally complemented lattices is generated by its simple members of finite length. A characterization of the class of simple unital Artinian members [members of finite length, respectively] of such varieties is given in the present paper.

Hereditary tensor-orthogonal theories

Pavel Jambor (1975)

Commentationes Mathematicae Universitatis Carolinae

Lattices of orthogonal theories

Jan Trlifaj (1989)

Czechoslovak Mathematical Journal

Currently displaying 41 – 60 of 181

Previous Page 3 Next