We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products. transformation semigroup, permutation group, wreath product, Krohn-Rhodes Theory

This work extends the Holcombe’s holonomy decomposition of near-rings to seminearrings employing the techniques of Eilenberg for studying the structure of transformation semigroups. This work investigates structural properties of certain types of seminearrings.

Using a variant of Schreier’s Theorem, and the theory of Green’s relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids...

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...

We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation α 7→ α, where α is the identity map on the domain of α. We investigate t...

decomposability of an algebraic structure into the :union: of its sub-structures goes back to g. scorza's theorem of 1926 for groups. an analogue of this theorem for rings has been recently studied by a. lucchini in 2012. on the study of this problem for non-group semigroups, the first attempt is due to clifford's work of 1961 for the regular semigroups. since then, n.p. mukherjee in ...

For a given reachable automaton A, we prove that the (state-)endomorphism monoid End(A) divides its characteristic monoid M(A). Hence so does its (state-)automorphism group Aut(A), and, for finite A, Aut(A) is a homomorphic image of a subgroup of the characteristic monoid. It follows that in the presence of a (state-) automorphism group G of A, a finite automaton A (and its transformation monoi...

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...