Glasnik Matematicki, Vol. 50, No. 2 (2015), 373-396.

THE VARIETY GENERATED BY ALL MONOIDS OF ORDER FOUR IS FINITELY BASED

Edmond W. H. Lee and Jian Rong Li

Department of Mathematics, Nova Southeastern University, Fort Lauderdale, Florida 33314, USA
e-mail: edmond.lee@nova.edu

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China
e-mail: lijr@lzu.edu.cn

Dedicated to Professor Mikhail V. Volkov on the occasion of his 60th birthday

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.

2010 Mathematics Subject Classification.   20M07.

Key words and phrases.   Monoid, semigroup, variety, finitely based.

Full text (PDF) (free access)

DOI: 10.3336/gm.50.2.08

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