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Certain Varieties and Quasivarieties of Completely Regular Semigroups

Published online by Cambridge University Press:  20 November 2018

Mario Petrich
Mario Petrich*
Affiliation:
Gesamthochschule Kassel, BR Deutschland
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We adopt the following definition of a completely regular semigroup S: for every element a of S, there exists a unique element a-1 of S such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1171 - 1197
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Birjukov, A. P., Varieties of idempotent semigroups, Algebra i Logika 9 (1970), 255-273 (in Russian); Transi. Algebra and Logic, Consult. Bureau 9 (1970), 153–164.Google Scholar
2. Clifford, A. H., Semigroups admitting relative inverses, Annals of Math. 42 (1941), 1037–1049.Google Scholar
3. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. I, Math. Surveys No. 7 (Amer. Math. Soc, Providence, 1961).Google Scholar
4. Evans, T., The lattice of semigroup varieties, Semigroup Forum 2 (1971), 1–43.Google Scholar
5. Fennemore, C. F., All varieties of bands, Math. Nachr. 48 (1971), I: 237-252, II: 253–262.Google Scholar
6. Gerhard, J. A., The lattice of equational classes of idempotent semigroups, J. Algebra 15 (1970), 195–224.Google Scholar
7. Gerhard, J. A. and Shafaat, A., Semivarieties of idempotent semigroups, Proc. London Math. Soc. (3) 22 (1971), 667–680.Google Scholar
8. Gràtzer, G., Universal algebra (Van Nostrand, Princeton, 1968).Google Scholar
9. Howie, J. M. and Lallement, G., Some fundamental congruences on a regular semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 145–156.Google Scholar
10. McAlister, D. B., Groups, semilattices and inverse semigroups, Trans. Amer. Math. Soc. 192 (1974), 227–244.Google Scholar
11. Neumann, H., Varieties of groups, Erg. Math. u.i. Grenzg. Vol. 37 (Springer, Berlin, 1967).Google Scholar
12. Petrich, M., Ùber Homomorphismen des direkten Produktes zweier Halbgruppen, Math. Nachr. 30 (1965), 230–235.Google Scholar
13. Petrich, M. Congruences on extensions of semigroups, Duke Math. J. SJf. (1967), 215–224.Google Scholar
14. Petrich, M. Introduction to semigroups (Merrill, Columbus, 1973).Google Scholar
15. Petrich, M. Regular semigroups which are subdirect product of a band and a semilattice of groups Glasgow J. Math. H(1973), 27–49.Google Scholar
16. Petrich, M. All subvarieties of a certain variety of semigroups, Semigroup Forum 7 (1974), 104–152.Google Scholar
17. Petrich, M. Varieties of orthodox bands of groups, Pacific J. Math. 58 (1975), 209–217.Google Scholar
18. Petrich, M. Lectures in semigroups (Akademie Verlag, Berlin, 1977).Google Scholar
19. Shafaat, A., On the structure of certain idempotent semigroups, Trans. Amer. Math. Soc. 149 (1970), 371–378.Google Scholar
20. Yamada, M., Note on idempotent semigroups, V: Implications of two variables, Proc. Japan Acad. 34 (1958), 668–671.Google Scholar