Factorizable semigroups

Tolo, Kenneth W.

doi:10.2140/pjm.1969.31.523

Cited by 29 publications

(13 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Naturally, similar constructions were sought for semigroups, and in particular for their most 'grouplike'classes. Thus what seems that the …rst usage of the term factorizable in the theory of semigroups was by Tolo [36], to mean S = AB = fab j a 2 A; b 2 Bg ; where A; B are subsemigroups of the semigroup S which are of special kinds, e.g., groups, completely semisimple, etc. 2 One may speculate that the reason Tolo's paper did not attract much attention is that his de…nition was broader than the one we use today-too general, one may say-even though his paper does consider the case of a chain of groups, which is a special case (group by chain) of the contemporary sense (group by semilattice).…”

Section: Some Historymentioning

confidence: 99%

Factorizable inverse monoids

FitzGerald

2009

Semigroup Forum

View full text Add to dashboard Cite

Factorizable inverse monoids constitute the algebraic theory of those partial symmetries which are restrictions of automorphisms; the formal de…nition is that each element is the product of an idempotent and an invertible. This class of monoids has theoretical signi…cance, and includes concrete instances which are important in various contexts. This survey is organised around the idea of group acts on semilattices and contains a large range of examples. Topics also include methods for construction of factorizable inverse monoids, and aspects of their inner structure, morphisms, and presentations.

show abstract

Section: Some Historymentioning

confidence: 99%

Factorizable inverse monoids

FitzGerald

2009

Semigroup Forum

View full text Add to dashboard Cite

show abstract

“…An element a of a hypergroupoid H is said to be a weak right (left) magnifying element of H if there exists a proper subset K of H such that H = K • a(H = a • K). Moreover, a is said to be a strong right (left) magnifying element of H if there exists a proper subhypergroupoid S of H such that H = S • a(H = a • S) [12].…”

Section: Preliminariesmentioning

confidence: 99%

Hypergroupoids as Tools for Studying Blood Group Genetics

Munir¹,

Kausar²,

Salahuddin³

et al. 2021

IJFIS

View full text Add to dashboard Cite

We initially introduce the concepts of an m-right (m-left) hyperideal and an m-hyperideal in a hypergroupoid. The ideas behind an m-factor and a generalized m-factor are then introduced. Next, we demonstrate the existence and important properties of these sub-hyperstructures through theorems and examples. We then define the m-right (m-left) consistent, m-consistent, m-intra-consistent, and m-simple hypergroupoids. Finally, we demonstrate that practical problems in biology, such as ABO blood group genetics, can be studied by defining these hypergroupoid substructures.

show abstract

“…The second part of the paper deals with the following problem proposed by the third author. Observe that in the founding paper of factorizable semigroups [26] the goal was to check when some given properties of A and B carry to the factorizable oversemigroup S := AB. Here we go in the converse direction: given T = SG, where S ≤ T n and G is the normalizer of S in S n , find semigroup properties that carry from SG to S. This looks a sensible question since in SG we can take advantage of the group theory machinery and hence checking a property might be easier in SG than in S.…”

Section: Introductionmentioning

confidence: 99%

Primitive permutation groups and strongly factorizable transformation semigroups

2021

View full text Add to dashboard Cite

Let Ω be a finite set and T (Ω) be the full transformation monoid on Ω. The rank of a transformation t ∈ T (Ω) is the natural number |Ωt|. Given A ⊆ T (Ω), denote by A the semigroup generated by A. Let k be a fixed natural number such that 2 ≤ k ≤ |Ω|. In the first part of this paper we (almost) classify the permutation groups G on Ω such that for all rank k transformations t ∈ T (Ω), every element in S t := G, t can be written as a product eg, where e 2 = e ∈ S t and g ∈ G. In the second part we prove, among other results, that if S ≤ T (Ω) and G is the normalizer of S in the symmetric group on Ω, then the semigroup SG is regular if and only if S is regular. (Recall that a semigroup S is regular if for all s ∈ S there exists s ∈ S such that s = ss s.) The paper ends with a list of problems.

show abstract

Factorizable semigroups

Cited by 29 publications

References 1 publication

Factorizable inverse monoids

Factorizable inverse monoids

Hypergroupoids as Tools for Studying Blood Group Genetics

Primitive permutation groups and strongly factorizable transformation semigroups

Contact Info

Product

Resources

About