Nearring π-Indecomposables and Ξ¦-Irreducibility
Year: 2024
Type: article
Abstract: This paper is mainly about direct summand right ideals of nearrings with π·πΆπΆπ which cannot be expressed as a non-trivial direct sum. A fairly natural condition (Ξ¦-irreducibility) makes it possible to study these right ideals in reasonable depth. It turns out they are either very ring like or right ideals (called shares) controlling considerable nearring structure. The two cases are studied in some detail. A surprising feature of the last section is that, with weak hypercentrality present, the nearring is a unique finite direct sum of these right ideals if, and only if, all such right ideals are ideals.
Source: Mathematica Pannonica
Author: Stuart D. Scott
Institution: University of Auckland
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404486225