Ordered semigroups and ideal categories of principal ideal rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913160459452416 |
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| author | Minnumol, P. K. Romeo, P. G. |
| author_facet | Minnumol, P. K. Romeo, P. G. |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25184 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ordered semigroups and ideal categories of principal ideal rings Minnumol, P. K. Romeo, P. G. Rings and Algebras 13E15 F.2.2 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 |
| title | Ordered semigroups and ideal categories of principal ideal rings |
| topic | Rings and Algebras 13E15 F.2.2 |
| url | https://arxiv.org/abs/2605.25184 |