Characterization of regular medial algebras

Representation of the Medial-Like Algebras

In this paper we characterize the regular medial algebras, the paramedial n-ary groupoids with a regular element, the paramedial algebras with a regular element and the regular paramedial algebras. Also, we characterize paramedial, co-medial and co-paramedial pairs of quasigroup operations and paramedial, co-medial and co-paramedial algebras with the quasigroup operations.

Arens regularity of inverse semigroup algebras‎

‎We present a characterization of Arens regular semigroup algebras‎ ‎$ell^1(S)$‎, ‎for a large class of semigroups‎. ‎Mainly‎, ‎we show that‎ ‎if the set of idempotents of an inverse semigroup $S$ is finite‎, ‎then $ell^1(S)$ is Arens regular if and only if $S$ is finite‎.

On Regular Co-Medial Algebras

In this paper we define the concepts of co-medial algebra and regular algebra and we will show that for a regular co-medial algebra (A, f , g), there exist a commutative semigroup (A,+), such that the operations f , g have the linear representation on (A,+). As a consequence of above result, we have the linear representation of an n−ary medial groupoid with an regular element, which was obtaine...

The Strong Amalgamation Property and (effective) Codescent Morphisms

Codescent morphisms are described in regular categories which satisfy the so-called strong amalgamation property. Among varieties of universal algebras possessing this property are, as is known, categories of groups, not necessarily associative rings, M -sets (for a monoid M), Lie algebras (over a field), quasi-groups, commutative quasi-groups, Steiner quasi-groups, medial quasigroups, semilatt...

Ergodic Theoretic Characterization of Left Amenable Lau Algebras