Substitution Principle and semidirect products

Proonite Categories and Semidirect Products

After developing a theory of implicit operations and proving an analogue of Reiterman's theorem for categories, this paper addresses two complementary questions for semidirect products and two-sided semidirect products of pseudovarieties of semigroups: to determine when a pseudoidentity is valid in it, and to nd a basis of pseudoidentities. The rst question involves looking into the structure o...

Semidirect Products of Ordered Semigroups

Semidirect products of ordered semigroups

We introduce semidirect and wreath products of finite ordered semigroups and extend some standard decomposition results to this case.

Semidirect Products of Association Schemes

In his 1996 work developing the theory of association schemes as a ‘generalized’ group theory, Zieschang introduced the concept of the semidirect product as a possible product operation of certain association schemes. In this paper we extend the semidirect product operation into the entire set of association schemes. We then derive a way to decompose certain association schemes into smaller ass...

Semidirect Products of Regular Semigroups

Within the usual semidirect product S ∗ T of regular semigroups S and T lies the set Reg (S ∗ T ) of its regular elements. Whenever S or T is completely simple, Reg (S ∗T ) is a (regular) subsemigroup. It is this ‘product’ that is the theme of the paper. It is best studied within the framework of existence (or e-) varieties of regular semigroups. Given two such classes, U and V, the e-variety U...