## Abstract

Let S be a Brandt semigroup in which the zero element is not externally adjoint. The question is: Under what conditions does a semigroup identity U=V (over a countable alphabet) which holds in one (hence in all) maximal group of S also hold in the whole semigroup S? This problem is completely solved by specifying necessary and sufficient conditions concerning the position of the letters in the words U and V. We omit the precise formulation of these rather complicated conditions.

The paper also contains the solution of the same problem for two other types of 0-simple semigroups.

Denote by ∏(φ) the variety of semigroups defined by a system of identities φ. One corollary (not proved in extenso) says: The class of 0-simple semigroups belonging to the variety ∏(xnyn=y2nx2n), n>1, is exactly the set of all Brandt semigroups over the groups of exponent n (=l.c.m. of the orders of the elements).

The paper also contains the solution of the same problem for two other types of 0-simple semigroups.

Denote by ∏(φ) the variety of semigroups defined by a system of identities φ. One corollary (not proved in extenso) says: The class of 0-simple semigroups belonging to the variety ∏(xnyn=y2nx2n), n>1, is exactly the set of all Brandt semigroups over the groups of exponent n (=l.c.m. of the orders of the elements).

Original language | Russian |
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Title of host publication | Semigroup varieties and semigroups of endomorphisms (Russian) |

Publisher | Leningrad. Gos. Ped. Inst., Leningrad |

Pages | 126-137 |

Number of pages | 12 |

State | Published - 1979 |