Glasnik Matematicki, Vol. 47, No. 2 (2012), 295-305.

EXCHANGE RINGS WITH MANY UNITS

Huanyin Chen

Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China
e-mail: huanyinchen@yahoo.cn

Abstract.   A ring R satisfies Goodearl-Menal condition provided that for any x,y R, there exists a u U(R) such that x-u,y-u-1 U(R). If R/J(R) is an exchange ring with primitive factors artinian, then R satisfies Goodearl-Menal condition if, and only if it has no homomorphic images Z/2Z, Z/3Z, M2 (Z/2Z). Exchange rings satisfying the primitive criterion are also studied.

2010 Mathematics Subject Classification.   16E50, 16U99.

Key words and phrases.   Goodearl-Menal condition, exchange ring, semilocal ring.

Full text (PDF) (free access)

DOI: 10.3336/gm.47.2.06

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