On finite regular rings

Robert Hartwig, Jiang Luh
1977 Pacific Journal of Mathematics  
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 R n x n , the n x n matrix ring over ring R, is unit regular, then so is the ring R. It is shown that if R 2 2 is finite
more » ... 2 is finite regular then a e R is unit regular if and only if there is x e R such that R -aRΛ-x(a°), where a 0 denotes the right annihilator of a in R.
doi:10.2140/pjm.1977.69.73 fatcat:oytpdflqbvhrjmv5blmjla4ioy