Medial idempotent groupoids III

Non-idempotent left symmetric left distributive groupoids

Subdirectly irreducible non-idempotent groupoids satisfying x · xy = y and x · yz = xy · xz are studied.

Finite idempotent groupoids and regular languages

Selfdistributive Groupoids. Part A2: Non-idempotent Left Distributive Left Quasigroups

The present paper is a comprehensive survey of non-indempotent left distributive left quasigroups. It contains several new results about free groupoids and normal forms of terms in certain subvarieties. It is a continuation of a series of papers on selfdistributive groupoids, started by [KepN,03].

On Varieties of Left Distributive Left Idempotent Groupoids

We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity x ≈ x decomposes as the direct product of its largest idempotent factor and a ...

Commutative, idempotent groupoids and the constraint satisfaction problem

A restatement of the Algebraic Dichotomy Conjecture, due to Maroti and McKenzie, postulates that if a finite algebra A possesses a weak near-unanimity term, then the corresponding constraint satisfaction problem is tractable. A binary operation is weak near-unanimity if and only if it is both commutative and idempotent. Thus if the dichotomy conjecture is true, any finite commutative, idempoten...