I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1996, VOLUME 2, NUMBER 1, PAGES 233-249
A. V. Tishchenko
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There are considered three different definitions of wreath product of semigroup varieties, namely: the general, monoidal and standard ones. It is shown that these are three different operations. An algorithm is found which gives us a possibility to decide if a given identity in a wreath product of semigroups is true provided such algorithms exist for initial semigroups. As a consequence of this result we get algorithms which give the answer to such question in monoidal, general and standard wreath product of semigroup varieties.
It is known that the monoidal and general wreath products of semigroup
varieties are associative.
It is proved that standard wreath product of semigroup varieties is
not associative even if the initial varieties are the atoms in the
lattice of all semigroup varieties.
The known variety generated by five-element completely
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