Centralizers and isomorphism preservation of minimal factors of nearring modules

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 preservati...

Full description

Saved in:
Bibliographic Details
Published inQuaestiones mathematicae Vol. 44; no. 7; pp. 923 - 944
Main Authors Peterson, Gary L., Scott, Stuart D.
Format Journal Article
LanguageEnglish
Published Grahamstown Taylor & Francis 03.07.2021
Taylor & Francis Ltd
Subjects
completely join irreducible
congruence preserving function
expanded group
Isomorphism
Modules
Nearring
Oil field equipment
Primary: 16Y30
Secondary: 06B10
tame module
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2020.1754957