When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become signi cantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-co...

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 1972 studied...

We study the complexity classes P and NP through a semigroup fP (“polynomial-time functions”), consisting of all polynomially balanced polynomial-time computable partial functions. Then P 6= NP iff fP is a non-regular semigroup. The one-way functions considered here are based on worstcase complexity (they are not cryptographic); they are the non-regular elements of fP. We prove various properti...

By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleannes present in the semilattice of idempotents of ...

The setting of this article is Classical algebra and Bishop’s constructive algebra (the algebra based on the Intuitionistic logic). The Esakia’s concept in the classical mathematics of strongly isotone mapping between ordered sets is extended onto two different concepts of mappings: on the concept of weakly isotone and the concept of strongly reverse isotone mapping of relational systems. Some ...

We give a new description of the fundamental double four-spiral semigroup. The fundamental four-spiral semigroup Sp4 and the fundamental double fourspiral semigroup DSp4 were introduced in [1], [3], and [4]. These semigroups are interesting examples of fundamental regular semigroups, and are indispensable building blocks of bisimple, idempotent-generated regular semigroups. Their basic properti...

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become significantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-c...

1. A. H. Clifford, Naturally totally ordered commutative semigroups, Amer. J. Math. 76(1954), 631-646. 2. , Totally ordered commutative semigroups, Bull. Amer. Math. Soc. 64 (1958), 305-316. 3. O. Holder, Die Axiome der Quantitât und die Lehre vom Mass, Ber. Verh. Sachs. Ges. Wiss. Leipzig Math.-Phys. Kl. 53 (1901), 1-64. 4. T. Tamura, Commutative nonpotent archimedean semigroup with cancellati...

Department of Mathematics, Jadavpur University Kolkata-700032, India manasi−[email protected] Abstract The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of Γsemigroups in order to obtain some characterization theorems. We also introduce the not...