On Ehresmann semigroups

Lawson, Mark V.

doi:10.1007/s00233-021-10200-2

Cited by 9 publications

(7 citation statements)

References 14 publications

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“…Let A and B be two right Ehresmann semigroups with distinguished semilattices E and F respectively. We recall (from [22]) that a right Ehresmann semigroup morphism from A to B is a semigroup homomorphism α : A → B such that for all x ∈ A, α(x ) = (α(x)) . If α is also bijective, then right Ehresmann semigroup morphism from A to B is an isomorphism.…”

Section: Preliminariesmentioning

confidence: 99%

On non-regular semigroups: $\lambda$-semidirect products, Zappa-Szép products and representations

ZAMAN

2024

Hacettepe Journal of Mathematics and Statistics

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This article encompasses the study of non-regular semigroups. First, we show that the $\lambda$-semidirect product $M \rtimes^{\lambda} W$ of a left $P$-Ehresmann semigroup $M$ and a left restriction semigroup $W$ is a left $P$-Ehresmann semigroup. We explore the behavior of generalized Green's relations on $M \rtimes^{\lambda} W$, and investigate some properties of $M \rtimes^{\lambda} W$. Second, the Zappa-Szép product of a right Ehresmann semigroup and its distinguished semilattice is studied. Lastly, the theory of representations of left Ehresmann semigroups with zero via homomorphisms of left Ehresmann semigroups with zero into Clifford restriction semigroups with zero is presented.

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Section: Preliminariesmentioning

confidence: 99%

On non-regular semigroups: $\lambda$-semidirect products, Zappa-Szép products and representations

ZAMAN

2024

Hacettepe Journal of Mathematics and Statistics

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“…Ehresmann semigroups appear naturally in the work on non-commutative Stone duality by Lawson and the first named author [21]. They are constructed from certain, localic or topological, étale categories and possess the additional structure of quantales, see also the recent work by Lawson [25] where a construction of Ehresmann semigroups from categories inspired by [21] is extensively studied.…”

Section: Introductionmentioning

confidence: 99%

“…Ehresmann semigroups and their one-sided analogues are widely studied non-regular generalizations of inverse semigroups, see, e.g. [2, 8, 10, 11, 16, 17, 21, 22, 25, 26, 32, 33]. They possess two unary operations and , which mimic the operations of taking the domain idempotent and the range idempotent in an inverse semigroup.…”

Section: Introductionmentioning

confidence: 99%

Proper Ehresmann semigroups

Kudryavtseva,

Laan

2023

Proceedings of the Edinburgh Mathematical Society

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We propose a notion of a proper Ehresmann semigroup based on a three-coordinate description of its generating elements governed by certain labelled directed graphs with additional structure. The generating elements are determined by their domain projection, range projection and σ-class, where σ denotes the minimum congruence that identifies all projections. We prove a structure result on proper Ehresmann semigroups and show that every Ehresmann semigroup has a proper cover. Our covering monoid turns out to be isomorphic to that from the work by Branco, Gomes and Gould and provides a new view of the latter. Proper Ehresmann semigroups all of whose elements admit a three-coordinate description are characterized in terms of partial multiactions of monoids on semilattices. As a consequence, we recover the two-coordinate structure result on proper restriction semigroups.

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“…Ehresmann semigroups and their one-sided analogues are widely studied non-regular generalizations of inverse semigroups, see, e.g., [2,7,9,10,15,16,20,21,24,28,31,32]. They possess two unary operations a → a + and a → a * which mimic the operations of taking the domain idempotent and the range idempotent in an inverse semigroup.…”

Section: Introductionmentioning

confidence: 99%

“…Ehresmann semigroups appear naturally in the work on non-commutative Stone duality by Lawson and the first named author [20]. They are constructed from certain, localic or topological, étale categories and possess the additional structure of quantales, see also the recent work by Lawson [24] where a construction of Ehresmann semigroups from categories inspired by [20] is extensively studied.…”

Section: Introductionmentioning

confidence: 99%

Proper Ehresmann semigroups

Kudryavtseva¹,

Laan²

2022

Preprint

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We propose a notion of a proper Ehresmann semigroup based on a threecoordinate description of its generating elements governed by certain labelled directed graphs with additional structure. The generating elements are determined by their domain projection, range projection and σ-class, where σ denotes the minimum congruence that identifies all projections. We prove a structure result on proper Ehresmann semigroups and show that every Ehresmann semigroup has a proper cover. Our covering semigroup turns out to be isomorphic to that from the work by Branco, Gomes and Gould and provides a new view of the latter. Proper Ehresmann semigroups all of whose elements admit a three-coordinate description are characterized in terms of partial multiactions of monoids on semilattices. As a consequence we recover the two-coordinate structure result on proper restriction semigroups.

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On Ehresmann semigroups

Cited by 9 publications

References 14 publications

On non-regular semigroups: $\lambda$-semidirect products, Zappa-Szép products and representations

On non-regular semigroups: $\lambda$-semidirect products, Zappa-Szép products and representations

Proper Ehresmann semigroups

Proper Ehresmann semigroups

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