Showing papers on "Bicyclic semigroup published in 2000"

Ordered Monoids and J-Trivial Monoids

Abstract: In this paper we give a new proof of the following result of Straubing and Therien: Every J-trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1.

Enlargements and Coverings by Rees Matrix Semigroups

Abstract: We formulate a general condition, called an enlargement, under which a semigroup T is covered by a Rees matrix semigroup over a subsemigroup.

A history of topological and analytical semigroups: a personal view

Abstract: and what nowadays, in more general form, is called domains, whileJ. D. LAWSON drew semigroup theoreticians' attention to a very natural class of compact semilattices having enough homomorphisms into the unit interval semilattice. The class of continuous lattices agrees with the class of Lawson semilattices. It generates a network of applications in theoretical computer science under the name "domain theory". - A hundred years after SOPHUS LIE's differentiable groups and semigroups, attention returned back to semigroups and Lie theory. Lie semigroup theory, initiated by E. B. VINBERG, G. I. OLSHANSKY, J. D. LAWSON and the author among others, infused a strong geometric and analytical flavor into topological semigroup theory and generated a new lines of application of semigroup theory such as in geometric control theory, and in the area of unitary representation theory of Lie groups, particulary in the area of holomorphic extensions of unitary representations. A respectable number of mongraphs and collections have been and are being written in this field.

The Representation Type of the Full Transforamtion Semigroup T4

Abstract: be the semigroup of all transformations of a set of n elements and k a field of characteristic 0. According to Ponizovskii, the semigroup algebra kT n is of finite representation type if n≤ 3. According to Putcha, kT n is of infinite representation type if n≥ 5. Here, we deal with the remaining case n=4 and show that kT 4 is also of finite representation type. Note that the quiver of kT 4 already has been exhibited by Putcha, here we determine the relations. It turns out that kT 4 is a string algebra and its global dimension is 3.

Equational bases for some 0-direct unions of semig oups

Abstract: In this paper,we investigate identities satis .ed by 0-direct unions of a semigroup with its anti-isomorphic copy,which serve as the standard tool for showing that an arbitrary semigroup can be embedded in (a semigroup reduct of)an involution semigroup.We show that,given the set of semigroup identities they satisfy,the involution de .ned on such 0-direct unions can be captured by only two additional identities involving the unary operation symbol.As a corollary of a result on .niteness of equational bases for such involution semigroups,we present an involution semigroup (which is,however,not an inverse one)consisting of 13 elements and not having a .nite equational basis.

Rank properties in finite inverse semigroups

Abstract: Abstract Two possible concepts of rank in inverse semigroup theory, the intermediate I-rank and the upper I-rank, are investigated for the finite aperiodic Brandt semigroup. The so-called large I-rank is found for an arbitrary finite Brandt semigroup, and the result is used to obtain the large rank of the inverse semigroup of all proper subpermutations of a finite set.

Topology of the Semigroup of Singular Endomorphisms

Abstract: of singular endomorphisms of an n-dimensional vector space over K are discussed here. Since S n is known to be an idempotent generated regular semigroup, we pay more attention to the topological properties of the set E n of idempotents in S n . The local structure of E n is shown to be that of a C infinity-manifold and of a finite-dimensional vector bundle over the Grassmann manifolds. The topology of the biorder relations and sandwich sets are also discussed.

The bracket semigroup of knots

Abstract: The paper is devoted to a coding of links with marked point on an oriented component by means of regular bibracket structures, ie, by some words in the alphabet (,),[,] In this way we naturally obtain the semigroup of knots with concatenation as the semigroup operation, and with the equivalence classes modulo so-called “global relations” as elements An important step in the construction of this semigroup is the coding of links with the help of so-calledd-diagrams

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.

A Generalization of C-semigroup

Abstract: In this paper, we define the concept of general C semigroup, which is an generalization of C semigroup The generator and the genertion of this general C semigroup are discussed Some examples and interesting applications are given too

Two-sided networks for completely simple semigroups

Abstract: Let S be a completely simple semigroup represented as a Rees matrix semigroup M(I,G,P) with normalized sandwich matrix P. On the congruence lattice C(S) of S we consider the relations T i, K and T r which identify congruences with the same left trace, kernel and right trace, respectively. These are equivalences whose classes are intervals. The upper and lower ends of these intervals induce the following operators on C(S) Tl, K, Tr, tl, k and tr .We construct here the semigroup generated by these operators as a homomorphic image of a semigroup given by generators and relations and demonstrate the minimality of the latter.