facni

valsi

facni

type

experimental gismu

creator

krtisfranks

time entered

Wed Feb 22 20:13:45 2017  

English

Definition #69387 - Preferred

 

definition

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.

notes

x₂ and x₃ 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 x₁. For any operator of x₂, x₁ is commutative with it with respect to functional composition (fa'ai) when the (other) operator is 'translated' to the corresponding operator of x₃ appropriately. x₁ is linear/a linear operator; x₁ is a homomorphism; x₁ distributes. x₂ is homomorphic with x₃ under x₁; 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 x₁ filled with "ce'u"; for "homomorphicity of spaces", use the same thing, but with x₂ or x₃ 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.

gloss words

• distributive function
• distributive operator
• distributive property
• graph homomorphism
• homomorphicity
• homomorphism ; algebra
• linear function ; linear algebra
• linear map ; vector space homomorphism
• linear operator

created by

krtisfranks

vote information

1

time

Fri Aug 12 17:55:36 2022

Examples

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