[PDF] Top 20 Automatic S acts and inverse semigroup presentations

... be automatic. Epstein et al. developed a theory of automatic groups, Campbell et ...an automatic group can be naturally extended to semigroups and investigated to what extent the theory of ... See full document

... As mentioned in Section 1, a classification of the finitely generated groups with an automatic presentation was given in [28]. For convenience, we state the result here (along with some extra details from [28] ... See full document

... Factorizable inverse monoids constitute the algebraic theory of those partial symmetries which are restrictions of automorphisms; the formal definition is that each element is the product of an idempotent and an ... See full document

... on presentations, see Stephen [16], [17] and ...an inverse word graph Γ over X is a connected graph with edges labeled over X ∪ X −1 , such that for every edge from v 1 to v 2 labeled by y, there is an ... See full document

... free inverse semigroups: two words u, v over X ∪ X −1 are equal in F I(X ) if and only if MT(u) = ...free inverse semigroup, we have e ≤ f if and only if the Munn tree of e can be embedded into the ... See full document

... A semigroup M is said to be factorizable if M = EG where E is a set of idempotents of M , and G is a subgroup of M ...factorizable inverse semigroups was initiated in ...factorizable inverse monoids ... See full document

... Investigation of finite generation and finite presentability of various constructions is one of the main areas of research in combinatorial semigroup theory. For example, finite generation and presentability of ... See full document

... The generating set Y is contained in the set TV = {1, 'ipjk, z : j. A: G {1,..., 2n}} and we will now show that AA is a monoid. The product of two transformations of the form 'ipjk is either a transformation of this form ... See full document

... the semigroup S is more complicated, one has to expect some conditions, since in general, automaticity of semigroups does depend on the choice of the generators (see ... See full document

... a semigroup S is defined to be |S−T ...in S is finite, then T is a large subsemigroup of S and S is a small extension of T ...for automatic presentations: the ... See full document

... One naturally asks whether the direct product of a free group and a polycyclic group is Malcev coherent. The present chapter answers this question negatively: indeed. Section 7.3 shows that polycyclic groups themselves ... See full document

... mutually inverse P-class preserving inner translations between the two corresponding ^-classes, Li and ...mutual inverse inner translations are ps,pt‘ One can easily show that Lr(77i) = Tr(772) via the ... See full document

... paper, S denotes a ...for S. Let A and B be left S-acts and let θ : A → B be an onto ...proper S-subact C of A, the restriction of θ to C is not ...left S-acts then ... See full document

... element s of a semigroup S is said to be indecomposable if s 6= uv for any u, v ∈ ...of S. Now suppose that S and T are infinite semigroups. If s ∈ S is ... See full document

... ∈ S , and a fuzzy ideal of S if f is both a fuzzy left and a fuzzy right ideal of ...a semigroup S if and only if f (xy) ≥ f (x) ∨f (y) for all x, y ∈ S , and that every fuzzy left ... See full document

... set s is a mapping of S X S into S, where S X S is defined as {(x, y)/x, y  S}; The image of (x, y) under this mapping is denoted by ... S. 2.2 A semigroup ... See full document

... ( S,+, .) be a semiring. If S contains a multiplicative identity which is also an absorbing element then a + b = a if and only if a + b + ab = a for all a, b in ... See full document

... The semigroup approach for inverse problems for the identification of unknown coefficient in a quasi-linear parabolic equations was studied by Demir and Ozbilge [, ... See full document

... the semigroup of linear operators by T (t) generated by the operator A [, ...the semigroup T(t) can be easily constructed by using the eigenvalues and eigenfunctions of the infinitesimal generator ... See full document

... ∈ S, a and Φ(Φ(a)) are both inverses of Φ(a) (that is, Φ(Φ(a))Φ(a)Φ(Φ(a)) = Φ(Φ(a)aΦ(a)) = Φ(Φ(a)) and Φ(a)Φ(Φ(a))Φ(a) = Φ(aΦ(a)a) = Φ(a)), so they are equal, by the uniqueness of ...∈ S such that Φ(b) = a ... See full document