Semigroups with operation-compatible Green’s quasiorders

The Lattice of Compatible Quasiorders of Acyclic Monounary Algebras

Acyclic monounary algebras are characterized by the property that any compatible partial order r can be extended to a compatible linear order. In the case of rooted monounary algebras A = (A, f ) we characterize the intersection of compatible linear extensions of r by several equivalent conditions and generalize these results to compatible quasiorders of A. We show that the lattice QuordA of co...

Rough Sets Determined by Quasiorders

In this paper, the ordered set of rough sets determined by a quasiorder relation R is investigated. We prove that this ordered set is a complete, completely distributive lattice, whenever the partially ordered set of the equivalence classes of R∩R−1 does not contain infinite ascending chains. We show that on this lattice can be defined three different kinds of complementation operations, and we...

Operads, quasiorders and regular languages

We generalize the construction of multi-tildes in the aim to provide double multitilde operators for regular languages. We show that the underlying algebraic structure involves the action of some operads. An operad is an algebraic structure that mimics the composition of the functions. The involved operads are described in terms of combinatorial objects. These operads are obtained from more pri...

Semigroups of rectangular matrices under a sandwich operation

Let Mmn =Mmn(F) denote the set of all m× n matrices over a field F, and fix some n×m matrix A ∈ Mnm. An associative operation ? may be defined on Mmn by X ? Y = XAY for all X,Y ∈ Mmn, and the resulting sandwich semigroup is denoted Mmn = Mmn(F). In this article, we study Mmn as well as its subsemigroups Reg(Mmn) and EA mn (consisting of all regular elements and products of idempotents, respecti...

Genes, greens, and homocysteine.