socnrpanrnji'akobi

valsi

socnrpanrnji'akobi

type

fu'ivla

creator

krtisfranks

time entered

Wed Feb 15 17:13:45 2023  

English

Definition #73146 - Preferred

 

definition

x₁ is a binary operator in structure x₂ which exhibits the Jacobi property with respect to binary operator x₃ (which also endows x₂) and element/object x₄ (which is an element of the underlying set which form x₂).

notes

This word uses a classifier which involves experimental gismu "socni" as a veljvo. Let x₁ be denoted by "f", x₂ be denoted by "X", x₃ be denoted by "+", and x₄ be denoted by "e". Then f exhibits the Jacobi property iff, for any x, y, z in X, the following is true: MATH

$f(x, f(y, z)) + f(z, f(x, y)) + f(y, f(z, x)) = e$

f (x, f (y, z)) + f (z, f (x, y)) + f (y, f (z, x)) = e. Notice that f may not be commutative; it may be necessary to further specify that e is the identity element in X for operstor '+', assuming that such is appropriate.

gloss words

• Jacobi property ; for binary operators; in a sense, it measures associativity.

created by

krtisfranks

vote information

1

time

Wed Feb 15 17:15:55 2023

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Examples

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