In this paper first we recall condition (PE) and then will give general properties a characterization of monoids for which all right acts satisfy condition. Finally, monoids, by comparing property their with some others.

Our aim in this paper is to study the concept of stability for acts over monoids and in the process develop a more coherent framework for some of the current techniques and construction used in the homological classification of monoids. We also present some new results relating to torsion free acts over monoids and to the embeddability of semigroup amalgams.

We discuss the model of valence grammars, a simple extension of context-free grammars. We show closure properties of context-free valence languages over arbitrary monoids. Chomsky and Greibach normal form theorems and an iteration lemma for context-free valence grammars over the groups Z are proved. The generative power of di4erent control monoids is investigated. In particular, we show that co...

For predual categories C andD we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these opfibrations are shown to correspond to varieties of languages in C, pseudovarieties of D-monoids, and profinite equational theories of D-monoids, respectively. As...

We consider the positive singular and the singular Artin monoids of finite type. These have been the subject of a great deal of recent research and the main purpose of this paper is to prove that these monoids are automatic. In order to do this we establish a new criterion for proving monoids automatic that may be of independent interest.

We show that the syntactic monoids of insertion-closed, deletionclosed and dipolar-closed languages are the groups. If the languages are insertionclosed and congruence simple, then their syntactic monoids are the monoids with disjunctive identity. We conclude with some properties of dipolarclosed languages.

We describe a class of monoids where c-rational languages can be deened analogously to trace theory and where these languages are precisely the recognizable ones. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to our left divisibility monoids. We obtain Ochma nski's theorem on recognizable languages in free partially commutative mo...

We consider certain decision problems for the free model of theory Cartesian monoids. introduce a computation based on notion single stack one-way PDA due to Ginsburg, Greibach and Harrison. This allows us solve such as (1) Given finite set B elements an element F, is F product members B? (2) Is submonoid generated by infinite? fragments monoid. These include right invertible so our results app...

We describe the inherently non-dualisable finite algebras from some semigroup related classes. The classes for which this problem is solved include the variety of bands, the pseudovariety of aperiodic monoids, commutative monoids, and (assuming a reasonable conjecture in the literature) the varieties of all finite monoids and finite inverse semigroups. The first example of an inherently non-dua...

There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems for three of these notions (which we will denote by ∼p, ∼o, and ∼c) in certain classes of finitely presented monoids. We will show that in the class of polycyclic monoids, p-conjugacy is “almost” transitive, ∼c is stric...