The varieties of semilattice-ordered semigroups satisfying x3 ≈ x and xy ≈ yx

被引：2

作者：

Ren, Miaomiao ^{[1
]}

Zhao, Xianzhong ^{[1
]}

机构：

[1] Northwest Univ, Sch Math, Xian 710127, Shaanxi, Peoples R China

来源：

PERIODICA MATHEMATICA HUNGARICA | 2016年 / 72卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Semilattice-ordered Burnside semigroup; Lattice; Subdirectly irreducible member; Variety; 0-Group; IDEMPOTENT SEMIRINGS; SUBVARIETIES;

D O I：

10.1007/s10998-016-0116-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to study the varieties of semilattice-ordered Burnside semigroups satisfying x(3) approximate to x and xy approximate to yx. It is shown that the collection of all such varieties forms a distributive lattice of order 9. Also, all of them are finitely based and finitely generated. This gives a generalization and expansion of the results obtained by McKenzie and Romanowska (Contrib Gen Algebra Proc Klagenf Conf 1978 1:213-218, 1979).

引用

页码：158 / 170

页数：13

共 10 条

[1] On varieties of semilattice-ordered semigroups
Kuril, M
Polák, L
SEMIGROUP FORUM, 2005, 71 (01) : 27 - 48
[2] The lattice of ai-semiring varieties satisfying xn ≈ x and xy ≈ yx
Ren, Miaomiao
Zhao, Xianzhong
Shao, Yong
SEMIGROUP FORUM, 2020, 100 (02) : 542 - 567
[3] The varieties of semilattice-ordered semigroups satisfying x3≈x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^3\approx x$$\end{document} and xy≈yx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$xy\approx yx$$\end{document}
Miaomiao Ren
Xianzhong Zhao
Periodica Mathematica Hungarica, 2016, 72 (2) : 158 - 170
[4] Admissible closure operators and varieties of semilattice-ordered normal bands
Kuřil M.
Acta Scientiarum Mathematicarum, 2017, 83 (1-2): : 35 - 50
[5] Varieties of Burnside ai-semirings satisfying xn ≈ x
Ren, Miaomiao
Zhao, Xianzhong
Shao, Yong
ACTA SCIENTIARUM MATHEMATICARUM, 2021, 87 (1-2): : 39 - 61
[6] ALGEBRAS SATISFYING THE POLYNOMIAL IDENTITY [x1, x2][x3, x4, x5]=0
Di Vincenzo, Onofrio M.
Drensky, Vesselin
Nardozza, Vincenzo
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2004, 3 (02) : 121 - 142
[7] On some varieties of ai-semirings satisfying xp+1 ≈ x
Wang, Aifa
Shao, Yong
OPEN MATHEMATICS, 2018, 16 : 913 - 923
[8] Varieties of Burnside ai-semirings satisfying xn ≈ x
Miaomiao Ren
Xianzhong Zhao
Yong Shao
Acta Scientiarum Mathematicarum, 2021, 87 : 39 - 61
[9] On the varieties of ai-semirings satisfying x3≈x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x^{3}\approx x}$$\end{document}
Miao Miao Ren
Xian Zhong Zhao
Ai Fa Wang
Algebra universalis, 2017, 77 (4) : 395 - 408
[10] The lattice of ai-semiring varieties satisfying xn≈x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^n\approx x$$\end{document} and xy≈yx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$xy\approx yx$$\end{document}
Miaomiao Ren
Xianzhong Zhao
Yong Shao
Semigroup Forum, 2020, 100 (2) : 542 - 567

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