A characterization of idempotent strong Mal’cev conditions for congruence meet-semidistributivity in locally finite varieties

For an arbitrary set X and an equivalence relation µ on X, denote by P µ (X) the semigroup of partial transformations α on X such that xµ ⊆ x(ker(α)) for every x ∈ dom(α), and the image of α is a partial transversal of µ. Every transversal K of µ defines a subgroup G = G K of P µ (X).We study subsemigroups G, U of P µ (X) generated by G ∪ U , where U is any set of elements of P µ (X) of rank less than |X/µ|. We show that each G, U is a regular semigroup, describe Green's relations and ideals in G, U , and determine when G, U is an inverse semigroup and when it is a completely regular semigroup. For a finite set X, the top J -class J of P µ (X) is a right group. We find formulas for the ranks of the semigroups J, G ∪ I, J ∪ I, and I, where I is any proper ideal of P µ (X).

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Semigroups of partial transformations with kernel and image restricted by an equivalence

André

Konieczny

2020

Semigroup Forum

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Solving CSPs Using Weak Local Consistency

Kozik¹

2021

SIAM J. Comput.

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Structure of principal one-sided ideals

East

2021

Int. J. Algebra Comput.

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A characterization of idempotent strong Mal’cev conditions for congruence meet-semidistributivity in locally finite varieties

Cited by 4 publications

References 20 publications

Semigroups of partial transformations with kernel and image restricted by an equivalence

Semigroups of partial transformations with kernel and image restricted by an equivalence

Solving CSPs Using Weak Local Consistency

Structure of principal one-sided ideals

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