Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic semigroup,soft neutosophic bisemigroup, soft neutrosophic N -semigroup with the discuissionf of some of their characteristics. We also introduced a new type of soft neutrophic semigroup, the so called soft strong neutrosophic semigoup which...

A variety V has an alg-universal n-expansion if the addition of n nullary operations to algebras from V produces an alg-universal category. It is proved that any semigroup variety V containing a semigroup that is neither an inflation of a completely simple semigroup nor an inflation of a semilattice of groups has an alg-universal 3-expansion. We say that a variety V is var-relatively alg-univer...

We define a cohomology theory for topological semigroups, with seminormed cohomology groups. Our theory can be considered as a topological version of bounded cohomology of discrete semigroups. 1. Definition of the cohomology Bounded cohomology was first defined for discrete groups by F. Trauber and then for topological spaces by M. Gromov [6]. In this paper we establish a topological bounded co...

The aim of this paper is to characterize the uniform exponential dichotomy of semigroups of linear operators in terms of the solvability of discrete-time equations over N. We give necessary and sufficient conditions for uniform exponential dichotomy of a semigroup on a Banach space X in terms of the admissibility of the pair (l∞(N, X), c00(N, X)). As an application we deduce that a C0-semigroup...

A semigroup is nilpotent of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree 3. We give formulae for the number of nilpotent semigroups of degree 3 on a set with n ∈ N elements up to equality, isomorphism, and isomorphism or ...

We study the number of solutions of the general semigroup equation in one variable, X α = X β , as well as of the system of equations X 2 = X, Y 2 = Y, XY = Y X in H ≀ T n , the wreath product of an arbitrary finite group H with the full transformation semigroup T n on n letters. For these solution numbers, we provide explicit exact formulae, as well as asymptotic estimates. Our results concern...

Notation 1.1. Let X be a projective variety over an algebraically closed field. For every integer k ≥ 0, denote by Nk(X) the finitely-generated free Abelian group of k-cycles modulo numerical equivalence, and denote by N(X) the k graded piece of the quotient algebra A∗(X)/Num∗(X), cf. [Ful98, Example 19.3.9]. For every Z-module B, denote Nk(X)B := Nk(X)⊗B, resp. N(X)B := N(X)⊗B. Denote by NEk(X...

In this paper we study commuting families of holomorphic mappings in Cn which form abelian semigroups with respect to their real parameter. Linearization models for holomorphic mappings are been used in the spirit of Schröder’s classical functional equation. The one-dimensional linearization models for holomorphic mappings and semigroups, based on Schröder’s and Abel’s functional equation have ...

A locally testable semigroup S is a semigroup with the property that for some nonnegative integer k, called the order or level of local testability, two words u and v in some set of generators for S are equal in the semigroup if (1) the pre x and su x of the words of length k coincide, and (2) the set of intermediate substrings of length k of the words coincide. The local testability problem fo...

We study the number of solutions of the general semigroup equation in one variable, X α = X β , as well as of the system of equations X 2 = X, Y 2 = Y, XY = Y X in H ≀ T n , the wreath product of an arbitrary finite group H with the full transformation semigroup T n on n letters. For these solution numbers, we provide explicit exact formulae, as well as asymptotic estimates. Our results concern...