Centralizers and isomorphism preservation of minimal factors of nearring modules

Abstract

If N1 is a nearring, V is a faithful tame N1-module and N2 is a nearring containing N1 such that V is a faithful tame N2-module and the N1- and N2-ideals of V coincide, we study when N1-isomorphic minimal factors of V are N2-isomorphic. We also study a stronger form of such preservation called type preservation. Par- ticular attention is paid to the case where N2 is the nearring of 0-preserving and congruence preserving functions of V , C0(V ). Here we will see that isomorphism preservation is related to centralizers of minimal factors relative to C0(V ) which then motivates the study of these centralizers as well.