Abstract
AbstractWe call a semigroup S f-noetherian if every right congruence of finite index on S is finitely generated. We prove that every finitely generated semigroup is f-noetherian, and investigate whether the properties of being f-noetherian and being finitely generated coincide for various semigroup classes.
Funder
University of St. Andrews
Publisher
Springer Science and Business Media LLC
Reference21 articles.
1. Bergman, G.: Problem list from algebras, lattices and varieties: a conference in honour of Walter Taylor, University of Colorado, 15–18 August, 2005. Algbra Universalis 55, 509–526 (2006)
2. Budach, L.: Strukter Noetherescher kommutativer Halbgruppen. Monatsberichte Deutschen Akad. Wiss. Berlin 6, 85–88 (1964)
3. Clifford, A., Preston, G.: The Algebraic Theory of Semigroups, vol. 2. American Mathematical Society, Providence (1967)
4. Gould, V.: Coherent monoids. J. Australian Math. Soc. 53, 166–182 (1992)
5. Dandan, Y., Gould, V., Quinn-Gregson, T., Zenab, R.: Semigroups with finitely generated universal left congruence. Monatschefte für Mathematik (2019)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. On minimal ideals in pseudo-finite semigroups;Canadian Journal of Mathematics;2022-11-15
2. Semigroups whose right ideals are finitely generated;Proceedings of the Edinburgh Mathematical Society;2021-10-01