Relational semigroups with domain and range are a useful tool for modelling nondeterministic programs. We prove that the representation class of domain-range demonic composition is not finitely axiomatisable. extend result ordered algebras show any relation algebra reduct signature containing domain, range, converse, composition, but no negation, meet, nor join has finite property. That represe...

We introduce the Favard spaces for resolvent families, extending some well-known theorems for semigroups. Furthermore, we show the relationship between these Favard spaces and the Lp-admissibility of control operators for scalar Volterra linear systems in Banach spaces, extending some results in [22]. Assuming that the kernel a(t) is a creep function which satisfies a(0+) > 0, we prove an analo...

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...

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 ...