J Austral Math Soc Ser A 59 pp173--183, 1995.
(Received 2 October 1992)
Given an R-module M, the centralizer near-ring MR(M) is the set of all functions f : M ® M with f(xr) = f(x)r for all x Î M and r Î R endowed with a point-wise addition and composition of functions as multiplication. In general, MR(M) is not a ring but is a near-ring containing the endomorphism ring ER(M) of M. Necessary and/or sufficient conditions are derived for MR(M) to be a ring. For the case that R is a Dedekind domain, the R-modules M are characterized for which (i) MR(M) is a ring; and (ii) MR(M) = ER(M). It is shown that over Dedekind domains with the finite prime spectrum properties (i) and (ii) are equivalent.
1991 AMS Subject Classification: 16D70, 16S50, 16Y30
Last Modified: Thu Jan 9 9:04:24 2003