Acta Mathematica Sinica, English Series
, Volume 29, Issue 3, pp 571590
First online:
On the finite basis problem for certain 2limited words
 Jian Rong LiAffiliated withDepartment of Mathematics, Lanzhou University
 , Wen Ting ZhangAffiliated withDepartment of Mathematics, Lanzhou University Email author
 , Yan Feng LuoAffiliated withDepartment of Mathematics, Lanzhou University
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Let X* be a free monoid over an alphabet X and W be a finite language over X. Let S(W) be the Rees quotient X*/I(W), where I(W) is the ideal of X* consisting of all elements of X* that are not subwords of W. Then S(W) is a finite monoid with zero and is called the discrete syntactic monoid of W. W is called finitely based if the monoid S(W) is finitely based. In this paper, we give some sufficient conditions for a monoid to be nonfinitely based. Using these conditions and other results, we describe all finitely based 2limited words over a threeelement alphabet. Furthermore, an explicit algorithm is given to decide that whether or not a 2limited word in which there are exactly two nonlinear letters is finitely based.
Keywords
Finite basis problem 2limited words discrete syntactic monoidMR(2000) Subject Classification
20M07 08B05 Title
 On the finite basis problem for certain 2limited words
 Journal

Acta Mathematica Sinica, English Series
Volume 29, Issue 3 , pp 571590
 Cover Date
 201303
 DOI
 10.1007/s1011401201931
 Print ISSN
 14398516
 Online ISSN
 14397617
 Publisher
 Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
 Additional Links
 Topics
 Keywords

 Finite basis problem
 2limited words
 discrete syntactic monoid
 20M07
 08B05
 Authors

 Jian Rong Li ^{(1)}
 Wen Ting Zhang ^{(1)}
 Yan Feng Luo ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Lanzhou University, Lanzhou, 730000, P. R. China