We define the length of a semigroup presentation and related ideas. Theoretical results and bounds are presented, gained while investigating the lengths of groups defined by semigroup presentations. Minimal length semigroup presentations are obtained in certain cases. AMS Mathematics Subject Classification (2000): 20F05, 20M05

Let S be a finite semigroup. In this paper we introduce the functions φs : S ∗ → S, first defined by Rhodes, given by φs([a1, a2, . . . , an]) = [sa1, sa1a2, . . . , sa1a2 · · · an]. We show that if S is a finite aperiodic semigroup, then the semigroup generated by the functions {φs}s∈S is finite and aperiodic.

For strongly continuous semigroups on a Hilbert space, we present a short proof of the fact that the left-inverse of a left-invertible semigroup can be chosen to be a semigroup as well. Furthermore, we show that this semigroup need not to be unique.

In this paper we have introduced fuzzy quasi-ideal and fuzzy left(right, two-sided) ideals in LA-semigroup. We have proved some results related to fuzzy quasi-ideals and fuzzy left(right, two-sided) ideals of an LA-semigroup. Further we characterize an intra-regular LA-semigroup by the properties of their fuzzy ideals.

We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover’s long-term private key. The latter is equivalent to solving the conjugacy search problem in the platform (noncommutative) semigroup, i.e., to recovering X from X−1AX and A. The platform semigroup that we suggest here is the semigroup of n×n matrices over truncated multivariable ...

and Applied Analysis 3 It is an interesting problem to extend the above results to a strongly continuous semigroup of nonexpansive mappings and a strongly continuous semigroup of asymptotically nonexpansive mappings. Let S be a strongly continuous semigroup of nonexpansive self-mappings. In 1998 Shioji and Takahashi 11 introduced, in Hilbert space, the implicit iteration

Let G be a semigroup of rational functions of degree at least two where the semigroup operation is composition of functions. We prove that the largest open subset of the Riemann sphere on which the semigroup G is normal and is completely invariant under each element of G, can have only 0, 1, 2, or infinitely many components.

In this paper we prove that if S is an irreducible numerical semigroup and S is generated by an interval or S has multiplicity 3 or 4, then it enjoys Toms decomposition. We also prove that if a numerical semigroup can be expressed as an expansion of a numerical semigroup generated by an interval, then it is irreducible and has Toms decomposition.