Not all nilpotent monoids are finitely related

被引：0
作者：
Markus Steindl
机构：
[1] Johannes Kepler University Linz,
[2] RISC Software GmbH,undefined
来源：
Algebra universalis | 2024年 / 85卷
关键词：
Semigroup; Term functions; Clone; Finitely related; Finite degree; Nilpotent; 20M07; 08A40; 20M05;
D O I：
暂无
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学科分类号：
摘要：
A finite semigroup is finitely related (has finite degree) if its term functions are determined by a finite set of finitary relations. For example, it is known that all nilpotent semigroups are finitely related. A nilpotent monoid is a nilpotent semigroup with adjoined identity. We show that every 4-nilpotent monoid is finitely related. We also give an example of a 5-nilpotent monoid that is not finitely related. To our knowledge, this is the first example of a finitely related semigroup where adjoining an identity yields a semigroup which is not finitely related. We also provide examples of finitely related semigroups which have subsemigroups, homomorphic images, and in particular Rees quotients, that are not finitely related.
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  • [1] Aichinger E(2010)Constantive Mal’cev clones on finite sets are finitely related Proc. Am. Math. Soc. 138 3501-3507
  • [2] Aichinger E(2014)On the number of finite algebraic structures J. Eur. Math. Soc. (JEMS) 16 1673-1686
  • [3] Mayr P(2013)Finitely related algebras in congruence distributive varieties have near unanimity terms Canad. J. Math. 65 3-21
  • [4] McKenzie R(2018)Finitely related algebras in congruence modular varieties have few subpowers J. Eur. Math. Soc. (JEMS) 20 1439-1471
  • [5] Barto L(2017)Deciding absorption in relational structures Algebra Univers. 78 3-18
  • [6] Barto L(2011)Finite degree: algebras in general and semigroups in particular Semigroup Forum 83 89-110
  • [7] Barto L(2018)Finite bands are finitely related Semigroup Forum 97 115-130
  • [8] Bulín J(1974)The structure of the upper neighborhood for predicate-describable classes in Dokl. Akad. Nauk SSSR 218 304-307
  • [9] Davey BA(2012)Finitely related clones and algebras with cube terms Order 29 345-359
  • [10] Jackson MG(2013)On finitely related semigroups Semigroup Forum 86 613-633
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