Relation algebras and function semigroups

Schein, Boris M.

doi:10.1007/bf02573019

Cited by 97 publications

(46 citation statements)

References 31 publications

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“…So together with the group laws, the above laws axiomatize fix-set quasi-orders on permutation groups. Such axiomatizations of semigroups of functions equipped with various additional quasi-orders or other binary relations have been considered over the years by a number of authors: see the survey papers [5] and [6] (although much work has been done since).…”

Section: Introduction and Summary Of Main Resultsmentioning

confidence: 99%

Groups with fix-set quasi-order

2015

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Abstract. If X is a set, the fix-set quasiorder on a group of permutations of X is the quasiorder induced by containment of the fix-sets of elements of S X . Axioms for such quasiorders on groups have previously been given. We generalise these to allow non-faithful group actions, the resulting abstract quasiorders being called fix-orders. We characterise the possible fix-orders on a given group G in terms of certain families of subgroups of G. The special case in which the members of the defining family of subgroups are all normal is considered. Software is used to construct and analyse the lattices of fix-orders of many small finite groups.

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Section: Introduction and Summary Of Main Resultsmentioning

confidence: 99%

Groups with fix-set quasi-order

2015

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“…It is not hard to verify that 1-stacks with identity element are term equivalent to twisted RC-semigroups where x 1 → C(x) and yC(x) → x y. A version of Proposition 2.1 is obtained for 1-stack semigroups in [18]. Lastly, we mention the work of Trokhimenko [22] who established an n-place function version of Proposition 2.1 (with n = 1 corresponding to the twisted RC-semigroups).…”

Section: Rc-semigroups Slorc's and Agreeablesmentioning

confidence: 98%

“…Both of these classes form quasivarieties generating the variety of twisted RC-semigroups (see [2]). Also closely related is the variety of 1-stacks, which are algebras in the operations of multiplication and ( [18]; see also Section IV, Example 17 of [19] for defining identities). It is not hard to verify that 1-stacks with identity element are term equivalent to twisted RC-semigroups where x 1 → C(x) and yC(x) → x y.…”

Section: Rc-semigroups Slorc's and Agreeablesmentioning

confidence: 99%

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Identities in the Algebra of Partial Maps

Jackson

Stokes

2006

Int. J. Algebra Comput.

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Abstract. We consider the identities of a variety of semigroup-related algebras modeling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.

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“…⊂} is a quasivariety [7], without loss of generality we may suppose that A is countable, i.e. A = {a 1 , a 2 , .…”

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confidence: 99%

On algebras of relations

Bredikhin

1993

Banach Center Publ.

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Throughout, by relation we mean a binary relation. Let Rel(X) be the set of all binary relations on the set X. An algebra of relations is a pair (Φ, Ω) where Ω is a set of operations on relations and Φ ⊂ Rel(X) is a set of relations closed under the operations of Ω. Each algebra of relations can be considered as ordered by the set-theoretic inclusion ⊂. Denote by M {Ω} the class of all algebras isomorphic to ones whose elements are relations and whose operations are members of Ω. The class M {Ω, ⊂} is determined in the same way.We will consider the following operations on relations: relation product •, relation inverse −1 , intersection ∩, diagonal relation ∆, and the unary operation *

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Relation algebras and function semigroups

Cited by 97 publications

References 31 publications

Groups with fix-set quasi-order

Groups with fix-set quasi-order

Identities in the Algebra of Partial Maps

On algebras of relations

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