The variety generated by all monoids of order four is finitely based

Edmond W. H. Lee; Jian Rong Li

doi:10.3336/gm.50.2.08

The variety generated by all monoids of order four is finitely based

Edmond W. H. Lee
, Jian Rong Li

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

It is known that the variety M_n generated by all monoids of order n is finitely based if n ≤ 3 and non-finitely based if n ≥ 6. The present article establishes the finite basis property of the variety M₄. This leaves M₅ as the last open case in the finite basis problem for the varieties M_n.

Original language	American English
Pages (from-to)	373–396
Journal	Glasnik Matematički
Volume	50
Issue number	2
DOIs	https://doi.org/10.3336/gm.50.2.08
State	Published - Dec 2015

Bibliographical note

Publisher Copyright:
© 2010 Mathematics Subject Classification.

ASJC Scopus Subject Areas

General Mathematics

Keywords

Monoid
Semigroup
Variety
Finitely based

Disciplines

Mathematics

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10.3336/gm.50.2.08

https://web.math.pmf.unizg.hr/glasnik/vol_50/no2_08.html

Cite this

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title = "The variety generated by all monoids of order four is finitely based",

abstract = "It is known that the variety Mn generated by all monoids of order n is finitely based if n ≤ 3 and non-finitely based if n ≥ 6. The present article establishes the finite basis property of the variety M4. This leaves M5 as the last open case in the finite basis problem for the varieties Mn.",

keywords = "Monoid, Semigroup, Variety, Finitely based",

author = "Lee, \{Edmond W. H.\} and Li, \{Jian Rong\}",

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AU - Lee, Edmond W. H.

AU - Li, Jian Rong

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N2 - It is known that the variety Mn generated by all monoids of order n is finitely based if n ≤ 3 and non-finitely based if n ≥ 6. The present article establishes the finite basis property of the variety M4. This leaves M5 as the last open case in the finite basis problem for the varieties Mn.

AB - It is known that the variety Mn generated by all monoids of order n is finitely based if n ≤ 3 and non-finitely based if n ≥ 6. The present article establishes the finite basis property of the variety M4. This leaves M5 as the last open case in the finite basis problem for the varieties Mn.

KW - Monoid

KW - Semigroup

KW - Variety

KW - Finitely based

UR - http://www.webofscience.com/wos/woscc/full-record/WOS:000367667100008

UR - https://www.scopus.com/pages/publications/84954235092

UR - https://www.scopus.com/pages/publications/84954235092#tab=citedBy

U2 - 10.3336/gm.50.2.08

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SP - 373

EP - 396

JO - Glasnik Matematički

JF - Glasnik Matematički

IS - 2

ER -

The variety generated by all monoids of order four is finitely based

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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