Displaying similar documents to “Definability for equational theories of commutative groupoids”

The ordering of commutative terms

Jaroslav Ježek (2006)

Czechoslovak Mathematical Journal

Similarity:

By a commutative term we mean an element of the free commutative groupoid F of infinite rank. For two commutative terms a , b write a ≤ b if b contains a subterm that is a substitution instance of a . With respect to this relation, F is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered...

Varieties of idempotent slim groupoids

Jaroslav Ježek (2007)

Czechoslovak Mathematical Journal

Similarity:

Idempotent slim groupoids are groupoids satisfying x x x ̄ and x ( y z ) x ̄ z . We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations.