Semigroup Forum

, Volume 95, Issue 1, pp 245–250 | Cite as

The identities of the free product of two trivial semigroups



We exhibit an example of a finitely presented semigroup S with a minimum number of relations such that the identities of S have a finite basis while the monoid obtained by adjoining 1 to S admits no finite basis for its identities. Our example is the free product of two trivial semigroups.


Semigroup identity Finitely based semigroup Nonfinitely based semigroup Zimin word 


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Hunter CollegeCity University of New YorkNew YorkUSA
  2. 2.Institute of Mathematics and Computer ScienceUral Federal UniversityEkaterinburgRussia

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