Semigroup Forum

, Volume 72, Issue 2, pp 159–189 | Cite as

Cryptic Semigroup Varieties

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Abstract

We describe all minimal noncryptic periodic semigroup [monoid] varieties. We prove that there are exactly three distinct maximal cryptic semigroup [monoid] varieties contained in the variety determined by xn ≈ x n+m, n ≥ 2, m ≥ 2. Analogous results are obtained for pseudovarieties: there are exactly three maximal cryptic pseudovarieties of semigroups [monoids]. It is shown that if a cryptic variety or pseudovariety of monoids contains a nonabelian group, then it consists of bands of groups only. Several characterizations are given of the cryptic overcommutative semigroup [monoid] varieties.

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and Computer Science, Marquette University, P.O.Box 1881, Milwaukee, WI 53201-1881USA
  2. 2.Department of Mathematics and Mechanics, Ural State University, Lenina 51, Ekaterinburg, 620083Russia

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