Finitely and non-finitely related words
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910513858871296 |
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| author | Glasson, Daniel |
| author_facet | Glasson, Daniel |
| contents | An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many interesting properties with respect to the finite basis problem. We show that much of this intriguing behaviour extends to the world of finite relatedness by using interlocking patterns called chain, crown, and maelstrom words. In particular, we show that there are large classes of non-finitely related nilpotent monoids that can be used to construct examples of: ascending chains of varieties alternating between finitely and non-finitely related; non-finitely related semigroups whose direct product are finitely related; the addition of an identity element to a non-finitely related semigroup to produce a finitely related semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finitely and non-finitely related words Glasson, Daniel Group Theory Rings and Algebras 20M07, 08A40 An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many interesting properties with respect to the finite basis problem. We show that much of this intriguing behaviour extends to the world of finite relatedness by using interlocking patterns called chain, crown, and maelstrom words. In particular, we show that there are large classes of non-finitely related nilpotent monoids that can be used to construct examples of: ascending chains of varieties alternating between finitely and non-finitely related; non-finitely related semigroups whose direct product are finitely related; the addition of an identity element to a non-finitely related semigroup to produce a finitely related semigroup. |
| title | Finitely and non-finitely related words |
| topic | Group Theory Rings and Algebras 20M07, 08A40 |
| url | https://arxiv.org/abs/2404.10203 |