Ordered semigroups and ideal categories of principal ideal rings
Rings and Algebras
2026-05-26 v1
Abstract
In this paper, we view the collection of ideals of a commutative principal ideal ring from two perspectives: one as an ordered semigroup I(R) and the other as a category I_R . It is shown that I(R) is a regular ordered semigroup whereas I_R is a category with subobjects. Further we establish the correspondence between these structure
Cite
@article{arxiv.2605.25184,
title = {Ordered semigroups and ideal categories of principal ideal rings},
author = {P. K. Minnumol and P. G. Romeo},
journal= {arXiv preprint arXiv:2605.25184},
year = {2026}
}
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13 pages 0 figures