#### 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, M*_{2} (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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