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arXiv · 2605.25184

Ordered semigroups and ideal categories of principal ideal rings

P. K. Minnumol·P. G. Romeo
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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

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P. K. Minnumol, P. G. Romeo. 2026-05-24. Ordered semigroups and ideal categories of principal ideal rings. https://arxiv.org/abs/2605.25184

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