Centralizers and isomorphism preservation of minimal factors of nearring modules

Abstract

If N ₁ is a nearring, V is a faithful tame N ₁-module and N ₂ is a nearring containing N ₁ such that V is a faithful tame N ₂-module and the N ₁- and N ₂-ideals of V coincide, we study when N ₁-isomorphic minimal factors of V are N ₂-isomorphic. We also study a stronger form of such preservation called type preservation. Particular attention is paid to the case where N ₂ is the nearring of 0-preserving and congruence preserving functions of V , C ₀(V ). Here we will see that isomorphism preservation is related to centralizers of minimal factors relative to C ₀(V ) which then motivates the study of these centralizers as well.