Bicyclic semigroup

About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.

Endomorphism seminear-rings of Brandt semigroups

Abstract: We consider the endomorphisms of a Brandt semigroup B n and the semigroup of mappings E(B n ) 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(B n ) for small n.

Classes of complete intersection numerical semigroups

Abstract: We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the logical implications among these classes and provide examples. Most of these classes are shown to be well-behaved with respect to the operation of gluing.

A group-embeddable non-automatic semigroup whose universal group is automatic

Abstract: Answering a question of Hoffmann and of Kambites, an example is exhibited of a finitely generated semigroup $S$ such that $S$ embeds in a group and $S$ is not automatic, but the universal group of $S$ is automatic.

Toric Mathematics from semigroup viewpoint

Abstract: Toric geometry is a subject of increasing activity. Toric varieties are objects on which one usually can check explicitly properties and compute invariants from algebraic geometry. This happens for the so-called normal toric varieties, i.e. algebraic varieties which are constructed from rational fans in an euclidean space. In the last 10 years the theory of non normal toric varieties has also been developed providing a very different and new scope as well as interesting and beautiful new applications. Normal toric geometry mainly uses techniques from convex geometry, as it is technically founded on the concepts of fan and cone. Fans are sets of polyhedral cones in such a way that each cone provides an affine chart of the toric variety. Namely, those charts have, as coordinate algebra, the algebra of the semigroup of lattice points lying inside the dual cone of the corresponding cone of the fan. To study non normal toric geometry one needs to be more precise than considers only cones. In fact, what one needs is to consider affine charts where coordinate algebras are semigroup ones for more general classes of semigroups. Thus, convex geometry should be used only as a tool by taking into account that nice semigroup generate concrete polyhedral cones. The purpose of this paper is to show how mathematics in toric geometry can be understood as the theory of appropriate classes of commutative semigroups with given generators. This viewpoint involves the description of various kinds of derived objects as abelian groups and lattices, algebras and binomial ideals, cones and fans, affine and projective algebraic varieties, simplicial and cellular complexes, polytopes, and arithmetics. Our approach consists in showing the mathematical relations among above objects and clarifying their possibilities for future developments in the area. For that purpose, we will survey some recent results and concrete applications.