Vol. 69, No. 1, 1977

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On finite regular rings

Robert E. Hartwig and Jiang Luh

Vol. 69 (1977), No. 1, 73–95

Several new properties are derived for von Neumann finite rings. A comparison is made of the properties of von Neumann finite regular rings and unit regular rings, and necessary and sufficient conditions are given for a matrix ring over a regular ring to be respectively von Neumann finite or unit regular. The converse of a theorem of Henriksen is proven, namely that if Rn×n, the n×n matrix ring over ring R, is unit regular, then so is the ring R. It is shown that if R2×2 is finite regular then a R is unit regular if and only if there is x R such that R = aR + x(a0), where a0 denotes the right annihilator of a in R.

Mathematical Subject Classification
Primary: 16A30, 16A30
Received: 17 August 1976
Revised: 1 October 1976
Published: 1 March 1977
Robert E. Hartwig
Jiang Luh