## Pacific Journal of Mathematics

- Pacific J. Math.
- Volume 132, Number 1 (1988), 151-175.

### Semigroups generated by certain operators on varieties of completely regular semigroups.

Mario Petrich and Norman R. Reilly

**Full-text: Open access**

#### Article information

**Source**

Pacific J. Math., Volume 132, Number 1 (1988), 151-175.

**Dates**

First available in Project Euclid: 8 December 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.pjm/1102689799

**Mathematical Reviews number (MathSciNet)**

MR929587

**Zentralblatt MATH identifier**

0598.20061

**Subjects**

Primary: 20M07: Varieties and pseudovarieties of semigroups

#### Citation

Petrich, Mario; Reilly, Norman R. Semigroups generated by certain operators on varieties of completely regular semigroups. Pacific J. Math. 132 (1988), no. 1, 151--175. https://projecteuclid.org/euclid.pjm/1102689799

#### References

- [9] Evaluation at the trivial variety. The diagram below presents a few varieties obtained by repeated application of the operators C,L? K, T,T and Tr to the trivial variety y . In order to save writing S' in the expressions of the form 3~C,3"T,3CTr, etc., we have written only C, ,Cr, etc. For example, the vertex labelled &= C = T stands for the variety of groups; this variety can also be described as 2C or 3T. The following legend is used to denote the classes induced by these operators:
- [1] R. Feigenbaum, Regular semigroup congruences, Semigroup Forum 17 (1979), 371-377.
- [2] J. A. Gerhard, Free completely regular semigroups II: Word Problem, J. Algebra, 82 (1983), 143-156.Mathematical Reviews (MathSciNet): MR84m:20063b
- [3] T. E. Hall, On regularsemigroups, J. Algebra, 24 (1973), 1-24.Mathematical Reviews (MathSciNet): MR46:9201
- [4] T. E. Hall and P. R. Jones, On the lattice of varieties of bands of groups, Pacific J. Math., 91 (1980), 327-337.
- [5] J. M. Howie, An Introduction to Semigroup Theory, Academic Press, London, 1976.
- [6] P. R. Jones, On the lattice of varieties of completely regular semigroups, J. Austral. Math. Soc, A35 (1983), 227-235.
- [7] P. R. Jones, Mal'cev products of varieties of completely regular semigroups, (preprint).
- [8] J. Kadourek, On the wordproblem for free bands of groups and for free objects in some other varieties of completely regular semigroups, Semigroup Forum, (to appear).
- [9] F. Pastijn and M. Petrich, The congruence lattice of a regular semigroup, (preprint).
- [10] F. J. Pastijn and P. G. Trotter, Lattices of completely regular semigroups, Pacific J. Math., 119 (1985), 191-214.
- [11] M. Petrich, Introduction to Semigroups, Merrill, Columbus, 1973.
- [12] M. Petrich and N. R. Reilly, Varieties of groups and of completely simple semigroups, Bull. Austral. Math. Soc, 23 (1981), 339-359.
- [13] N. R. Reilly, Varieties of completely regular semigroups. J. Austral. Math. Soc, A38 (1985), 372-393.

#### Pacific Journal of Mathematics, A Non-profit Corporation

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