We consider the endomorphisms of a Brandt semigroup Bn, and the semigroup of mappings E(Bn) that they generate under pointwise composition. We describe all the elements of this semigroup, determine Green’s relations, consider certain special types of mapping which we can enumerate for each n, and give complete calculations for the size of E(Bn) for small n. AMS 2000 Mathematics subject classifi...

We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with nonnegative coefficients and the semigroup Dn of all doubly stochastic real matrices.

In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, the...

In this paper we investigate the relation between discrete and continuous operators. More precisely, we investigate the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger...

This is a survey paper on algorithms that have been developed during the last 25 years for the explicit computation of the structure of an associative algebra of finite dimension over either a finite field or an algebraic number field. This constructive approach was initiated in 1985 by Friedl and Rónyai and has since been developed by Cohen, de Graaf, Eberly, Giesbrecht, Ivanyos, Küronya and W...

a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...

This paper studies the integers that belong the multiplicative semigroup W generated by { 2n+1 : n ≥ 0} and 1 2 . They form a multiplicative semigroup W(Z) of integers which we call the wild integer semigroup, and the wild numbers are the generators of W(Z). It presents convincing evidence that the wild numbers consist of all prime numbers excluding 3.

Semigroups whose congruences form a chain are often termed ∆-semigroups. The commutative ∆-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative ∆-semigroups. It turns out that there are only six noncommutative exampl...

We study parameter spaces of linear series on projective curves in the presence unibranch singularities, i.e. cusps; and to do so, we stratify cusps according value semigroup. show that generalized Severi varieties maps P1→Pn with images fixed degree arithmetic genus are often reducible whenever n≥3. also prove variety degree-d a hyperelliptic cusp delta-invariant g≪d is codimension at least (n...