Algebraic properties of Zappa–Szép products of semigroups and monoids

Zenab, Rida-e

doi:10.1007/s00233-017-9878-1

Cited by 9 publications

(17 citation statements)

References 23 publications

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“…Now suppose E has definable meets. Then for s ∈ S and e, f ∈ E, Assuming definable meets, the fact that E is as described is easily seen, as is the fact that for (e, s) [24]). However, this is not a special case of our result since S equipped with the above action is not a modal left E-monoid even if S has identity, since s • 1 = D(s) rather than 1.…”

Section: Connection With the Zappa-szép Productmentioning

confidence: 99%

“…Very generally, one may define an external Zappa-Szép product of semigroups if each acts on the other in a certain way. We here follow the notational conventions used in [24], modified to have some notational similarity with the current situation. Thus suppose S, E are semigroups with multiplication in S denoted by juxtaposition and in E by ∧, and that we have actions S × E → E given by (s, e) → s • e, and S × E → S given by (s, e) → s e , satisfying the following four conditions: for all s, t ∈ S and e, f ∈ E,…”

Section: Connection With the Zappa-szép Productmentioning

confidence: 99%

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Left restriction monoids from left $E$-completions

Stokes¹

2021

Preprint

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Given a monoid S with E any non-empty subset of its idempotents, we present a novel one-sided version of idempotent completion we call left E-completion. In general, the construction yields a one-sided variant of a small category called a constellation by Gould and Hollings. Under certain conditions, this constellation is inductive, meaning that its partial multiplication may be extended to give a left restriction semigroup, a type of unary semigroup whose unary operation models domain. We study the properties of those pairs S, E for which this happens, and characterise those left restriction semigroups that arise as such left E-completions of their monoid of elements having domain 1. As first applications, we decompose the left restriction semigroup of partial functions on the set X and the right restriction semigroup of left total partitions on X as left and right E-completions respectively of the transformation semigroup T X on X, and decompose the left restriction semigroup of binary relations on X under demonic composition as a left E-completion of the left-total binary relations. In many cases, including these three examples, the construction embeds in a semigroup Zappa-Szép product.

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Section: Connection With the Zappa-szép Productmentioning

confidence: 99%

Section: Connection With the Zappa-szép Productmentioning

confidence: 99%

Left restriction monoids from left $E$-completions

Stokes¹

2021

Preprint

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“…In [18] Zenab describe generalized Green's relations for the general product of semigroups and monoids. In this section we aim to characterize generalized Green's relations on generalized general product.…”

Section: Generalized Green's Relations On Generalized General Productsmentioning

confidence: 99%

The Arithmetic of Generalization for General Products of Monoids

Wazzan

2021

Comm. Math Appl.

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For A and B arbitrary monoids. In a recent work, Cevik et al. (Hacettepe Journal of Mathematics and Statistics 50(1) (2021), 224 -234) defined new consequence of the general product denoted by A ⊕B δ ψ B ⊕A and gave a presentation for this generalization.In this paper, we explore the way in which the structure of the generalization of general product reflects the properties of its associated wreath products.

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“…As a next step of the studies in [11,17,20], in this section, we will study on some Green's relations for generalized general product A ⊕B δ ψ B ⊕A .…”

Section: Some Green's Relations On Generalized General Productmentioning

confidence: 99%

Some algebraic structures on the generalization general products of monoids and semigroups

2020

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For arbitrary monoids A and B, in Cevik et al. (Hacet J Math Stat 2019:1–11, 2019), it has been recently defined an extended version of the general product under the name of a higher version of Zappa products for monoids (or generalized general product) $$A^{\oplus B}$$ A ⊕ B $$_{\delta }\bowtie _{\psi }B^{\oplus A}$$ δ ⋈ ψ B ⊕ A and has been introduced an implicit presentation as well as some theories in terms of finite and infinite cases for this product. The goals of this paper are to present some algebraic structures such as regularity, inverse property, Green’s relations over this new generalization, and to investigate some other properties and the product obtained by a left restriction semigroup and a semilattice.

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Algebraic properties of Zappa–Szép products of semigroups and monoids

Cited by 9 publications

References 23 publications

Left restriction monoids from left $E$-completions

Left restriction monoids from left $E$-completions

The Arithmetic of Generalization for General Products of Monoids

Some algebraic structures on the generalization general products of monoids and semigroups

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