x_{1} is an n-ary operator/map which is distributive/linear/homomorphic in or over or from space/structure x_{2}, mapping to space or structure x_{3}, thereby producing a new space/structure x_{4} which is the 'union' of x_{2} and x_{3} endowed with x_{1}; x_{1} distributes over/through all of the operators of x_{2}.

x_{2} and x_{3} cannot merely be sets; they must be structures/systems which each are a set/category endowed with at least one operator/relation/property (here, "operator" will refer to any of these options) each; the ith operator endowing one space corresponds to exactly the ith operator endowing the other space under mapping x_{1}. For any operator of x_{2}, x_{1} is commutative with it with respect to functional composition (fa'ai) when the (other) operator is 'translated' to the corresponding operator of x_{3} appropriately. x_{1} is linear/a linear operator; x_{1} is a homomorphism; x_{1} distributes. x_{2} is homomorphic with x_{3} under x_{1}; they need not be identical (in fact, their respective operators need not even be identical, just 'homomorphically similar'). For "distributivity"/"distributive property", "linearity of operator", or "homomorphicity of operator", use "ka(m)( )facni" with x_{1} filled with "ce'u"; for "homomorphicity of spaces", use the same thing, but with x_{2} or x_{3} filled with "ce'u". See also: "socni", "cajni", "sezni", "dukni"; "fa'ai"; "fatri". This is a structure-operator-preserving function, and thus is an example of a stodraunju.

- cajni
- x
_{1}is a binary operator which is commutative in space/under conditions/on (or endowing) set x_{2}; x_{1}and x_{2}are each abelian (in different senses). - dukni
- x
_{1}is a binary operator in space/under conditions/on (or endowing) set x_{2}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. - stodraunju
- x
_{1}is a function mapping x_{2}(domain) to x_{3}(codomain) such that properties x_{4}(ka) of x_{2}are preserved in its image under x_{1}according to the rules/operations/relations of x_{3}corresponding to those of x_{2}by x_{1}.