Finite basis problem for Annular monoids with rotation

被引：0
|
作者：
Zhang, Wen Ting [1 ]
Han, Bin Bin [1 ,2 ]
Luo, Yan Feng [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[2] Changzhou Univ, Dept Math, Changzhou 213164, Jiangsu, Peoples R China
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年
基金：
中国国家自然科学基金;
关键词：
Partition monoids; annular monoids; involution; finite basis problem; identity; SEMIGROUPS;
D O I：
10.1142/S0219498825503360
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (U-n,(rho)) be the involution monoid of Annular monoid U-n under the rotation involution rho. The involution monoids (U-1,(rho)) and (U-2,(rho)) are easily seen to be finitely based; Auinger et al. proved that (U-n,(rho)) is inherently non-finitely based if n >= 4. In this paper, we show that (U-3,(rho)) is finitely based by providing a finite identity basis for (U-3,(rho)), which answers an open question posed by Auinger et al. Therefore, the involution monoid (U-n,(rho)) is finitely based if and only if n <= 3.
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页数：19
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