Finite basis problem for Catalan monoids with involution

Author:

Gao Meng12,Zhang Wen Ting1,Luo Yan Feng1

Affiliation:

1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China

2. Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg 620000, Russia

Abstract

It is known, since the early 2000s, that the Catalan monoid [Formula: see text] generated by [Formula: see text] elements is finitely based if and only if [Formula: see text]. The main goal of this paper is to prove that the involution monoid [Formula: see text] is non-finitely based. Therefore, in contrast, combining with previous results yields that the involution Catalan monoid [Formula: see text] is finitely based if and only if [Formula: see text]. The Kiselman monoid [Formula: see text] generated by [Formula: see text] elements is also considered. Although the semigroups [Formula: see text] and [Formula: see text] have recently been shown to satisfy the same identities, it is unknown if the same result holds when they are considered as involution semigroups. Nevertheless, it is deduced from the main result that the involution Kiselman monoid [Formula: see text] is finitely based if and only if [Formula: see text].

Funder

National Natural Science Foundation of China

Natural Science Foundation of Gansu Province

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Cited by 3 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

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