In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...

Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open subset U ⊂ S to a family of stable curves over S. More precisely, we introduce the abelian monodromy extension (AME) property and show that the standard Deligne-Mumford compactification is the unique, maximal AME compactification of the moduli space of curves. We also show ...

We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free...

Inspired by the results of [APR], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebr...

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a “landscape” of string/M theory vacua, perhaps containing many candidates for describing r...

We call (T (t))t≥0 an abstract delay semigroup. This notion is introduced in more detail in Section 2. The semigroup thus obtained is rarely a contraction semigroup. In this paper we will show that under very mild conditions, we may change the inner product on E into an equivalent inner product, such that the delay semigroup becomes a (generalized) contraction semigroup. A contraction semigroup...

Left-discrimination of a semigroup is defined and shown to be a sufficient condition that a semigroup be isomorphic to the input semigroup of its semigroup automaton, a necessary condition if the semigroup is finite. The left-discrimination sequence of an automaton is defined as a sequence of semigroups beginning with the input semigroup of the automaton, each member being the input semigroup o...

We present a polynomial-time reduction of the discrete logarithm problem in any periodic (a.k.a. torsion) semigroup (Semigroup DLP) to the classic DLP in a subgroup of the same semigroup. It follows that Semigroup DLP can be solved in polynomial time by quantum computers, and that Semigroup DLP has subexponential algorithms whenever the classic DLP in the corresponding groups has subexponential...

We systematically analyze regularization of different kinds of ultradistribution semigroups and sines, in general, with nondensely defined generators and contemplate several known results concerning the regularization of Gevrey type ultradistribution semigroups. We prove that, for every closed linear operator A which generates an ultradistribution semigroup (sine), there exists a bounded inject...

The interaction of automatic semigroups and Bruck–Reilly extensions is studied. It is proved that every automatic Bruck–Reilly extension has an automatic base semigroup. This result is then applied to answer negatively the question of Andrade et al. on whether automatic structures for Bruck–Reilly extensions of groups are characterized by the fellow traveller property. An example is exhibited t...