HNN extensions of semigroups

Dekov, Deko V.

doi:10.1007/bf02573473

Cited by 8 publications

(4 citation statements)

References 8 publications

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“…Clearly the morphism λ i is locally surjective and bijective on the sets of the vertices. Furthermore, M i and N i are approximate automata of SΓ (S[φ, t e ], u) and SΓ (S φ, t , θ 2 (u)), respectively, by Lemma 4.2 (2). Therefore, (P1), (P2) and (P3) are satisfied for i.…”

Section: (53)mentioning

confidence: 57%

“…The most important property of this construction is that S is naturally embedded into S(φ, t). This is classified as an HNN extension of type I in [14] and the restricted case that the stable letter belongs to the group of units is discussed in [1,2,6,8,9]. This construction is applied to several algorithmic problems like the undecidability of Markov properties of inverse semigroups in [15,18].…”

Section: Presentation S(φ T)mentioning

confidence: 97%

“…One such generalization is studied in [1,2,6,8,9] where a stable letter belongs to the group of units. It can also be generalized to the class of inverse semigroups in a way that stable letters are not necessarily a group element.…”

Section: Introductionmentioning

confidence: 99%

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Embedding theorems for HNN extensions of inverse semigroups

Yamamura

2007

Journal of Pure and Applied Algebra

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A variant of an HNN extension of an inverse semigroup introduced by Gilbert [N.D. Gilbert, HNN extensions of inverse semigroups and groupoids, J. Algebra 272 (2004) 27-45] is defined provided that associated subsemigroups are order ideals. We show this presentation still makes sense without the assumption on associated subsemigroups in the sense that it gives a semigroup deserving to be an HNN extension, and it is embedded into another variant using the automata theoretical technique based on combinatorial and geometrical properties of Schützenberger graphs.

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Section: (53)mentioning

confidence: 57%

Section: Presentation S(φ T)mentioning

confidence: 97%

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Embedding theorems for HNN extensions of inverse semigroups

Yamamura

2007

Journal of Pure and Applied Algebra

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“…We now examine the properties of M in some detail. First, we observe that the presentation looks very similar to that of an HNN extension (see [13,26]). Indeed, M is obviously a quotient of the HNN extension with presentation…”

Section: Appendix Amentioning

confidence: 83%

Covers for monoids

Fountain

Weil

2004

Journal of Algebra

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A monoid M is an extension of a submonoid T by a group G if there is a morphism from M onto G such that T is the inverse image of the identity of G. Our first main theorem gives descriptions of such extensions in terms of groups acting on categories.The theory developed is also used to obtain a second main theorem which answers the following question. Given a monoid M and a submonoid T , under what conditions can we find a monoid M and a morphism θ from M onto M such that M is an extension of a submonoid T by a group and θ maps T isomorphically onto T .These results can be viewed as generalisations of two seminal theorems of McAlister in inverse semigroup theory. They are also closely related to Ash's celebrated solution of the Rhodes conjecture in finite semigroup theory.McAlister proved that each inverse monoid admits an E-unitary inverse cover and gave a structure theorem for E-unitary inverse monoids. Many researchers have extended one or both of these results to wider classes of semigroups. Almost all these generalisations can be recovered from our two main theorems.

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Deciding embeddability of partial groupoids into semigroups

Dekov¹

1999

Semigroup Forum

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HNN extensions of semigroups

Cited by 8 publications

References 8 publications

Embedding theorems for HNN extensions of inverse semigroups

Embedding theorems for HNN extensions of inverse semigroups

Covers for monoids

Deciding embeddability of partial groupoids into semigroups

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