cajni experimental gismu

x₁ is a binary operator which is commutative in space/under conditions/on (or endowing) set x₂; x₁ and x₂ are each abelian (in different senses).

Denote x₁ by "♤"; for any elements x,y in the set of concern, if '♤' is commutative, then x♤y = y♤x, where equality is defined in the space. "Commutative property"/"commutativity" = "ka(m)( )cajni". See also: socni, sezni, dukni, facni.

jbovlaste

In notes:

dukni: x₁ is a binary operator in space/under conditions/on (or endowing) set x₂ such that there is an identity element and for any element for which it is defined in the space (excepting possibly a small number of special elements), there exists at least one element also in the space which is a left-inverse of that element under the operator.
facni: x₁ is an n-ary operator/map which is distributive/linear/homomorphic in or over or from space/structure x₂, mapping to space or structure x₃, thereby producing a new space/structure x₄ which is the 'union' of x₂ and x₃ endowed with x₁; x₁ distributes over/through all of the operators of x₂.