Cancellative semigroup

About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.

On the lattice of congruences on an eventually regular semigroup

Abstract: A natural equivalence 6 on the lattice of congruences A(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that 0 is a congruence, each 0-class is a complete sublattice of A(S)-and the maximum element in each 0-class is determined.

Commutative semigroups with cancellation law: a representation theorem

Abstract: Any commutative, cancellative semigroup S with 0 equipped with a uniformity can be embedded in a topological group \(\widetilde{S}\). We introduce the notion of semigroup symmetry T which enables us to turn \(\widetilde{S}\) into an involutive group. In Theorem 2.8 we prove that if S is 2-torsion-free and T is 2-divisible then the decomposition of elements of \(\widetilde{S}\) into a sum of elements of the symmetric subgroup \(\widetilde{S}_{s}\) and the asymmetric subgroup \(\widetilde{S}_{a}\) is polar. In Theorem 3.7 we give conditions under which a topological group \(\widetilde{S}\) is a topological direct sum of its symmetric subgroup \(\widetilde{S}_{s}\) and its asymmetric subgroup \(\widetilde{S}_{a}\). Theorem 2.8 and Theorem 3.7 are designed to be useful tools in studying Minkowski–Radstrom–Hormander spaces (and related topological groups \(\widetilde{S}\)), which are natural extensions of semigroups of bounded closed convex subsets of real Hausdorff topological vector spaces.

Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on

Abstract: We prove that if a Borel probability measure on the circle group is invariant under the action of a �large� multiplicative semigroup (lower logarithmic density is positive) and the action of the whole semigroup is ergodic then the measure is either Lebesgue or has finite support

A mealy machine with polynomial growth of irrational degree

Abstract: We consider a very simple Mealy machine ( two nontrivial states over a two-symbol alphabet), and derive some properties of the semigroup it generates. It is an infinite, finitely generated semigroup, and we show that the growth function of its balls behaves asymptotically like l(alpha), for alpha = 1 + log 2/log 1+root 5/2 ; that the semigroup satisfies the identity g(6) = g(4); and that its lattice of two-sided ideals is a chain.

WE-m semigroups.

Abstract: In this chapter we deal with semigroups in which, for every elements a and b, there is a non-negative integer k such that (ab) m+k =a m b m =(ab) k a m b m , where m is a fixed i n te g er m ≥ 2. These se m igrou p s are c a lled WE- m se m igroups. It is clear that every E-m semigroup is a WE-m semigroup. The examination of WE-m semigroups need some results about E-m semigroups. Thus the E-m semigroups were examined in the previous chapter. As a WE-m semigroup is a left and right Putcha semigroup, it is a semilattice of WE-m archimedean semigroups. We show that the 0-simple WE-mn semigroups are the completely simple E-m semigroups with a zero adjoined. A semigroup is a WE-m archimedean semigroup containing at least one idempotent element if and only if it is a retract extension of a completely simple E-m semigroup by a nil semigroup. We also prove that every WE-2 archimnedean semigroup without idempotent element has a non-trivial group homomorphic image. We deal with the regular WE-m semigroups. We show that the regular WE-m semigroups are exactly the regular exponential semigroups. Moreover, we show that a semigroup which is an ideal extension of a regular semigroup K by a nil sernigroup N is a WE-2 semigroup if and only if K is an E-2 semigroup and the extension is retract. We deal with the subdirectly irreducible WE-2 semigroups.