In this article we consider semigroups of transformations of cellular automata which act on a fixed shift space. In particular, we are interested in two properties of these semigroups which relate to “largeness”. The first property is ID and the other property is maximal commutativity (MC). A semigroup has the ID property if the only infinite invariant closed set (with respect to the semigroup ...

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...

The relative rank rank(S : A) of a subset A of a semigroup S is the minimum cardinality of a set B such that 〈A ∪ B〉 = S. It follows from a result of Sierpiński that, if X is infinite, the relative rank of a subset of the full transformation semigroup TX is either uncountable or at most 2. A similar result holds for the semigroup BX of binary relations on X. A subset S of TN is dominated (by U)...

Let α be a Zd–action (d ≥ 2) by automorphisms of a compact metric abelian group. For any non–linear shape I ⊂ Zd, there is an α with the property that I is a minimal mixing shape for α. The only implications of the form “I is a mixing shape for α =⇒ J is a mixing shape for α” are trivial ones for which I contains a translate of J . If all shapes are mixing for α, then α is mixing of all orders....

It is known that a left C-wrpp semigroup can be described as curler structure of a left band and a C-wrpp semigroup. In this paper, we introduce the class of weakly left C-wrpp semigroups which includes the class of weakly left C-rpp semigroups as a subclass. We shall particularly show that the spined product of a left C-wrpp semigroup and a right normal band is a weakly left C-wrpp semifroup. ...

The paper shows how some semigroup-theory methods can be used in automata problems. The theory of automata is closely connected with the theory of semigroups (or, to be more exact, with the theory of representations of semigroups by transformations). The concept of automaton without outputs is equivalent to the concept of representa­ tion of free semigroup by transformations. If we consider eve...

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

In this paper we compute the minimal degree of a faithful representation by partial transformations finite semigroup admitting completely reducible matrix over field complex numbers. This includes all inverse semigroups, and hence our results generalize earlier Easdown Schein on an semigroup. It also well-studied monoids like full fields monoid binary relations (i.e., matrices Boolean semiring)...

Rank 1 transformations serve as a source of examples in ergodic theory showing variety algebraic, asymptotic, and spectral properties dynamical systems. The rank one transformation are closely related to the structure semigroup weak limits its powers. In this vein, known new constructions studied.

Let ⌦ be a set of cardinality n, G a permutation group on ⌦, and f : ⌦ ! ⌦ a map which is not a permutation. We say that G synchronizes f if the semigroup hG, fi contains a constant map. The first author has conjectured that a primitive group synchronizes any map whose kernel is non-uniform. Rystsov proved one instance of this conjecture, namely, degree n primitive groups synchronize maps of ra...