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. Particular 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.

Mathematics Subject Classification (2010):

• Primary: 16Y30
• Secondary: 06B10
• 08A30

Key words:

• Nearring
• tame module
• expanded group
• congruence preserving function
• completely join irreducible