Semidirect products of semigroups

Preston, G. B.

doi:10.1017/s0308210500014505

Cited by 17 publications

(21 citation statements)

References 4 publications

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“…Necessary and sufficient conditions for T fl x 5 to be regular, again extending a result of Nico [2], were found in [3], Theorem 5. Applied to the situation in which 5…”

Section: (Ts) (T S J = (Tt^ssj supporting

confidence: 58%

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The semidirect product of an inverse semigroup and a group

Preston

1986

Bull. Austral. Math. Soc.

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“…Necessary and sufficient conditions for T fl x 5 to be regular, again extending a result of Nico [2], were found in [3], Theorem 5. Applied to the situation in which 5…”

Section: (Ts) (T S J = (Tt^ssj supporting

confidence: 58%

“…and T are inverse Theorem 5 of [3] simplifies to PROPOSITION 1. Let S and T be inverse semigroups and 9.…”

Section: (Ts) (T S J = (Tt^ssj mentioning

confidence: 99%

The semidirect product of an inverse semigroup and a group

Preston

1986

Bull. Austral. Math. Soc.

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“…For semigroups there is no such universal correspondence between internal and external Zappa-Szép products and indeed not even for semidirect products, as remarked by Preston [20]. Preston went on to provide, by judicious adding of identities, a way to move between internal and external semidirect products of semigroups, but the correspondence is weaker than that in the case for monoids [20]. A similar correspondence in the case of Zappa-Szép products of semigroups is given in the thesis of the author [26].…”

Section: (S T)(s T ) = (S(t · S ) T S T )mentioning

confidence: 98%

“…Conversely if Z = ST is the internal Zappa-Szép product of submonoids S and T then uniqueness of decompositions and associativity enable us to show that Z is isomorphic to an external Zappa-Szép product S T . For semigroups there is no such universal correspondence between internal and external Zappa-Szép products and indeed not even for semidirect products, as remarked by Preston [20]. Preston went on to provide, by judicious adding of identities, a way to move between internal and external semidirect products of semigroups, but the correspondence is weaker than that in the case for monoids [20].…”

Section: (S T)(s T ) = (S(t · S ) T S T )mentioning

confidence: 99%

Algebraic properties of Zappa–Szép products of semigroups and monoids

Zenab

2017

Semigroup Forum

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Direct, semidirect and Zappa-Szép products provide tools to decompose algebraic structures, with each being a natural generalisation of its predecessor. In this paper we examine Zappa-Szép products of monoids and semigroups and investigate generalised Greens relations R * , L * , R E and L E for these Zappa-Szép products. We consider a left restriction semigroup S with semilattice of projections E and define left and right actions of S on E and E on S, respectively, to form the Zappa-Szép product E S. We further investigate properties of E S and show that S is a retract of E S. We also find a subset T of E S which is left restriction.

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“…[17], we give the concept of the left wreath products. We shall show that an L * -inverse semigroup can be expressed as a left wreath product of a type A semigroup and a left regular band.…”

Section: Introductionmentioning

confidence: 99%

The structure of ℒ*-inverse semigroups

Ren

Shum

2006

SCI CHINA SER A

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The concepts of L * -inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L * -inverse semigroup can be described as the left wreath product of a type A semigroup Γ and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L * -inverse semigroups by using the left wreath products.

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Semidirect products of semigroups

Abstract: SynopsisTwo alternative characterizations of semidirect products of semigroups are given. Characterizations are provided of such products that are groups, regular semigroups, and inverse semigroups, respectively.

Cited by 17 publications

References 4 publications

The semidirect product of an inverse semigroup and a group

The semidirect product of an inverse semigroup and a group

Algebraic properties of Zappa–Szép products of semigroups and monoids

The structure of ℒ*-inverse semigroups

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