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Embedding torsionless modules in projectives.

Carl Faith (1990)

Publicacions Matemàtiques

In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring Rn is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.

Exchange rings in which all regular elements are one-sided unit-regular

Huanyin Chen (2008)

Czechoslovak Mathematical Journal

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 ∈ R , there exist an e ∈ E ( R ) and a u ∈ U ( R ) such that a = e + u and a R ∩ e R = 0 if and only if for any regular a ∈ R , there exist e ∈ r . a n n ( a + ) and u ∈ U ( R ) such that a = e + u if and only if for any a , b ∈ R , R / a R ≅ R / b R ⟹ a R ≅ b R .

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 , ⋯ , 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.

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