Jörg Koppitz

ON THE MAXIMAL SUBSEMIGROUPS OF SOME TRANSFORMATION SEMIGROUPS

Let Singn be the semigroup of all singular transformations on an n-element set. We consider two subsemigroups of Singn: the semigroup On of all isotone singular transformations and the semigroup Mn of all monotone singular transformations. We describe the maximal subsemigroups of these two semigroups, and study the connections between them.

Essential variables in hypersubstitutions

Abstract. For a variety V of algebras of type

The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain

\tau

POWER CLONES AND NON-DETERMINISTIC HYPERSUBSTITUTIONS

, we consider the set Mi(V) of all hypersubstitutions

MULTI-HYPERSUBSTITUTIONS AND COLORED SOLID VARIETIES

\sigma

EQUATIONAL THEORIES GENERATED BY HYPERSUBSTITUTIONS OF TYPE (n)

such that the variable xi is essential in the term

Hyperassociative Varieties of Semigroups

\sigma

On the semigroup of all partial fence-preserving injections on a finite set

(f) with respect to the variety V. We will give a complete answer to the question for which varieties V of type

Maximal subsemigroups containing a particular semigroup

\tau

CATEGORY EQUIVALENCES OF CLONES OF OPERATIONS PRESERVING UNARY OPERATIONS

= (n) the set Mi(v) of hypersubstitutions forms a monoid. This is important since to every monoid of hypersubstitutions there corresponds a complete sublattice of the lattice of all varieties of algebras of the given type. For varieties of semigroups we get the monoid of all leftmost and all rightmost hypersubstitutions.