Centralizers and isomorphism preservation of minimal factors of nearring modules. Issue 7 (3rd July 2021)

• Record Type: Journal Article
• Authors: Peterson, Gary L.; Scott, Stuart D.
• Is Part Of: Quaestiones mathematicae. Volume 44:Issue 7(2021)
• Page Start: 923
• Page End: 944
• Publication Date: 2021-07-03
• Subjects: Primary: 16Y30 -- Secondary: 06B10 -- 08A30; Nearring -- tame module -- expanded group -- congruence preserving function -- completely join irreducible; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2020.1754957
• Languages: English
• ISSNs: 1607-3606

Abstract

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.