a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

It is well-known that B2 is an inverse 0-simple semigroup that has played a distinguished role in the theory of semigroups. Let B2 be the variety generated by B2, and let B0 be the variety generated by the subsemigroup B0 = {0, d, cd, dc} of B2. Since all semigroups with five or fewer elements are finitely based [5], the variety B2 and its subvariety B0 are finitely based. In fact, it has been ...

We discuss the relationship between tight and cover-to-join representations of semilattices inverse semigroups, showing that a slight extension former, together with an appropriate selection codomains, makes two notions equivalent. As consequence, when constructing universal objects based on them, one is allowed to substitute for vice-versa.

Classifications of (α,β )-fuzzy left (right and lateral) ideals of ternary semigroups are discussed. Relations between (∈,∈ ∨q)-fuzzy left (right and lateral) ideals and (q,∈∨q)-fuzzy left (right and lateral) ideals are established. Given special sets, so called t-q-set and t-∈∨q-set, conditions for the t-q-set and t-∈∨q-set to be left (right and lateral) ideals are considered. Conditions for a...

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...

The problem of decidability of membership in the semidirect product Sl L of the pseudovarieties Sl of all nite semilattices and L of all nite L-trivial semigroups has been around since 1984. This paper discusses several developments motivated by this question and leading to a proof that settles it aarmatively.