Weakly right coherent monoids
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910849249050624 |
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| author | Dasar, Levent Michael Gould, Victoria Miller, Craig |
| author_facet | Dasar, Levent Michael Gould, Victoria Miller, Craig |
| contents | A monoid $S$ is said to be weakly right coherent if every finitely generated right ideal of $S$ is finitely presented as a right $S$-act. It is known that $S$ is weakly right coherent if and only if it satisfies the following conditions: $S$ is right ideal Howson, meaning that the intersection of any two finitely generated right ideals of $S$ is finitely generated; and the right annihilator congruences of $S$ are finitely generated as right congruences. We examine the behaviour of these two conditions (in the more general setting of semigroups) under certain algebraic constructions and deduce closure results for the class of weakly right coherent monoids. We also show that the property of being right ideal Howson is related to the axiomatisability of a class of left acts satisfying a condition related to flatness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly right coherent monoids Dasar, Levent Michael Gould, Victoria Miller, Craig Rings and Algebras 20M12, 20M30, 03C55 A monoid $S$ is said to be weakly right coherent if every finitely generated right ideal of $S$ is finitely presented as a right $S$-act. It is known that $S$ is weakly right coherent if and only if it satisfies the following conditions: $S$ is right ideal Howson, meaning that the intersection of any two finitely generated right ideals of $S$ is finitely generated; and the right annihilator congruences of $S$ are finitely generated as right congruences. We examine the behaviour of these two conditions (in the more general setting of semigroups) under certain algebraic constructions and deduce closure results for the class of weakly right coherent monoids. We also show that the property of being right ideal Howson is related to the axiomatisability of a class of left acts satisfying a condition related to flatness. |
| title | Weakly right coherent monoids |
| topic | Rings and Algebras 20M12, 20M30, 03C55 |
| url | https://arxiv.org/abs/2411.03947 |