On finitary power monoids of linearly orderable monoids
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912178580226048 |
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| author | Dani, Jiya Gotti, Felix Hong, Leo Li, Bangzheng Schlessinger, Shimon |
| author_facet | Dani, Jiya Gotti, Felix Hong, Leo Li, Bangzheng Schlessinger, Shimon |
| contents | A commutative monoid $M$ is called a linearly orderable monoid if there exists a total order on $M$ that is compatible with the monoid operation. The finitary power monoid of a commutative monoid $M$ is the monoid consisting of all nonempty finite subsets of $M$ under the so-called sumset. In this paper, we investigate whether certain atomic and divisibility properties ascend from linearly orderable monoids to their corresponding finitary power monoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On finitary power monoids of linearly orderable monoids Dani, Jiya Gotti, Felix Hong, Leo Li, Bangzheng Schlessinger, Shimon Commutative Algebra Primary: 13A05, 13F15, Secondary: 13A15, 13G05 A commutative monoid $M$ is called a linearly orderable monoid if there exists a total order on $M$ that is compatible with the monoid operation. The finitary power monoid of a commutative monoid $M$ is the monoid consisting of all nonempty finite subsets of $M$ under the so-called sumset. In this paper, we investigate whether certain atomic and divisibility properties ascend from linearly orderable monoids to their corresponding finitary power monoids. |
| title | On finitary power monoids of linearly orderable monoids |
| topic | Commutative Algebra Primary: 13A05, 13F15, Secondary: 13A15, 13G05 |
| url | https://arxiv.org/abs/2501.03407 |