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arXiv · 2501.03407

On finitary power monoids of linearly orderable monoids

Jiya Dani·Felix Gotti·Leo Hong·Bangzheng Li·Shimon Schlessinger
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Abstract

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.

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Jiya Dani, Felix Gotti, Leo Hong, Bangzheng Li, Shimon Schlessinger. 2025-01-06. On finitary power monoids of linearly orderable monoids. https://arxiv.org/abs/2501.03407

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