We introduce the notion of admissible transfomations which is related to the Hungarian method for solving assignment problems. Admissible transformations are stated for linear, quadratic and multi-index assignment problems. Their application to find good lower bounds and/or to solve the problem, respectively, is outlined. Finally it is shown that admissible transformations can also be applied t...

Let 5( + , < ) be a system consisting of a set S endowed with an associative binary operation + and a total ( = linear = simple) order relation < . The composition + and the relation < may be connected by either or both of the following conditions. MC (Monotone Condition). If a and b are elements of 5 such that ax+y ...

Carrying on the work of Arnold, Pécuchet and Perrin, Wilke has obtained a counterpart of Eilenberg’s variety theorem for finite and infinite words. In this paper, we extend this theory for classes of languages that are closed under union and intersection, but not necessarily under complement. As an example, we give a purely algebraic characterization of various classes of recognizable sets defi...

Let A be a simple, unital, finite, and exact C-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomorphism, and prove the conjecture in several cases. In these same cases — Z-stab...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

It is well known that the right (left) regular, regular, and intra-regular ordered semigroups play an essential role in studying the structure, especially the decomposition, of ordered semigroups. In the present paper we study some more general classes containing the right regular, left regular, regular and intra-regular ordered semigroups. As an application of our results we get characterizati...

Fuzzy semigroup theory concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an ( , )-fuzzy filter of an ordered semigroup , where , , , , with . Since the concept of ( , )-fuzzy filter is an important and useful generalization of ordinary fuzzy filter,...

Let X denote a complete separable metric space, and let C(X) denote the linear space of all bounded continuous real-valued functions on X. The Lie generator of a strongly continuous semigroup T of continuous transformations in X is the linear operator in C(X) consisting of all ordered pairs (f; g) such that f; g 2 C(X), and for each x 2 X, g(x) is the derivative at 0 of f(T()x). We completely c...

The semigroup of binary relations on {1, . . . , n} with the relative product is isomorphic to the semigroup Bn of n×n matrices over {0, 1} with the Boolean matrix product. Over any field F , we prove that there is an ideal Kn in FBn of dimension (2n−1)2, and we construct an explicit isomorphism of Kn with the matrix algebra M2n−1(F ). Let Zn = {1, . . . , n} (n ≥ 1); then P (Z n), the power se...