Let ~ C be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category ~ C is called ~ C-closed if for each morphism Φ ⊂ X×Y in the category ~ C the image Φ(X) = {y ∈ Y : ∃x ∈ X (x, y) ∈ Φ} is closed in Y. In the paper we survey existing and new results on topological groups, which are ~...

We initiate the study of interval-valued fuzzy quasi-ideal of a semigroup. In Section 2, we list some basic definitions in the later sections. In Section 3, we investigate interval-valued fuzzy subsemigroups and in Section 4, we define intervalvalued fuzzy quasi-ideals and establish some of their basic properties. In Section 5, we obtain characterizations of regular and intraregular semigroups ...

It has been well known that the band of idempotents of a naturally ordered orthodox semigroup satisfying the “strong Dubreil-Jacotin condition” forms a normal band. In the literature, the naturally ordered orthodox semigroups satisfying the strong Dubreil-Jacotin condition were first considered by Blyth and Almeida Santos in 1992. Based on the name “epigroup” in the paper of Blyth and Almeida S...

We analyze cohomological properties of the Krichever map and use the results to study Weierstrass cycles in moduli spaces and the tautological ring. Let us consider a point p on a smooth projective connected curve C over C of genus g. We say that a natural number n is a non-gap if there exists a function that is holomorphic on C \p and has a pole of order n at the point p (in other words h0(O(n...

The syntactic semigroup problem is to decide whether a given finite semigroup is syntactic or not. This work investigates the syntactic semigroup problem for both the semigroup reducts of A(Bn), the affine nearsemiring over a Brandt semigroup Bn. It is ascertained that both the semigroup reducts of A(Bn) are syntactic semigroups.

On any set X may be defined the free algebra R〈X〉 (respectively, free commutative algebra R[X]) with coefficients in a ring R. It may also be equivalently described as the algebra of the free monoid X∗ (respectively, free commutative monoid M (X)). Furthermore, the algebra of differential polynomials R{X} with variables inX may be constructed. The main objective of this contribution is to provi...

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We comp...

Let (S,+) be an infinite commutative semigroup with identity 0. Let u, v ∈ N and let A be a u×v matrix with nonnegative integer entries. If S is cancellative, let the entries of A come from Z. Then A is image partition regular over S (IPR/S) iff whenever S \{0} is finitely colored, there exists ~x ∈ (S \{0}) such that the entries of A~x are monochromatic. The matrix A is centrally image partiti...