FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 3, PAGES 889-902

A wreath product of semigroups and varieties of finite index

A. V. Tishchenko

Abstract

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We have found the necessary and sufficient conditions on semigroups under which their extended standard wreath product generates a variety of finite index. Further, the similar problem is solved for varieties of completely simple semigroups. Finally, the necessary and sufficient conditions on monoid $S$ are found under which the endomorphism monoid of a free left act over $S$ generates a variety of finite index.

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Last modified: December 8, 2000