Czechoslovak Mathematical Journal, Vol. 55, No. 2, pp. 273-281, 2005

Extensions of $GM$-rings

Huanyin Chen, Miaosen Chen

H. Chen, M. Chen, Dept. of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P.R. China, e-mails: chyzxl@sparc2.hunnu.edu.cn, miaosen@mail.jhptt.zj.cn

Abstract: It is shown that a ring $R$ is a $GM$-ring if and only if there exists a complete orthogonal set $\{e_1,\cdots,e_n\}$ of idempotents such that all $e_iRe_i$ are $GM$-rings. We also investigate $GM$-rings for Morita contexts, module extensions and power series rings.

Keywords: $GM$-ring, module extension, power series ring

Classification (MSC 2000): 16U99, 16E50


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