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Medial groupoids

Definition

A \emph{medial groupoid} is a structure G=G,, where is an infix binary operation such that

mediates: (xy)(zw)=(xz)(yw)

Morphisms

Let G and H be medial groupoids. A morphism from G to H is a function h:GH that is a homomorphism:

h(xy)=h(x)h(y)

Jaroslav Jezek, Tomas Kepka,\emph{Equational theories of medial groupoids}, Algebra Universalis, \textbf{17}1983,174–190MRreview

Jaroslav Jezek, Tomas Kepka,\emph{Medial groupoids}, Rozpravy Ceskoslovenske Akad. Ved Rada Mat. Prirod. Ved, \textbf{93}1983,93MRreview

Examples

Example 1: S,, where S,+, is any commutative semiring, a,bS, and xy=ax+by.

Basic results

Properties

Finite members

f(1)=1f(2)=f(3)=f(4)=f(5)=f(6)=f(7)=

Subclasses

Superclasses

References


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