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Keywords:
regular semigroup; orthodox semigroup; inverse semigroup; e–variety; biinvariant congruence
regular semigroup; orthodox semigroup; inverse semigroup; e–variety; biinvariant congruence
Summary:
We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.
References:
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[2] Hall, T. E.: Identities for existence varieties of regular semigroups. Bull. Austral. Math. Soc. 40 (1989), 59-77. MR 1020841 | Zbl 0666.20028
[3] Howie, J. M.: An Introduction to Semigroup Theory. Academic Press, London, 1976. MR 0466355 | Zbl 0355.20056
[4] Kaďourek, J., Szendrei, M. B.: A new approach in the theory of orthodox semigroups. Semigroup Forum 40 (1990), 257-296. MR 1038007
[5] Pol k, L.: A multiplication on the lattice of varieties of $*$-regular semigroups. to appear in Proceedings of Luino International Conference on Semigroups.
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