Editing Algebraic structure (section)

===Equational axioms===
An axiom of an algebraic structure often has the form of an [[identity (mathematics)|identity]], that is, an [[equation (mathematics)|equation]] such that the two sides of the [[equals sign]] are [[expression (mathematics)|expressions]] that involve operations of the algebraic structure and [[variable (mathematics)|variables]]. If the variables in the identity are replaced by arbitrary elements of the algebraic structure, the equality must remain true. Here are some common examples.
;[[Commutativity]]: An operation <math>*</math> is ''commutative'' if <math display = block>x*y=y*x </math> for every {{mvar|x}} and {{mvar|y}} in the algebraic structure.
;[[Associativity]]: An operation <math>*</math> is ''associative'' if <math display = block>(x*y)*z=x*(y*z) </math> for every {{mvar|x}}, {{mvar|y}} and {{mvar|z}} in the algebraic structure.
;[[Left distributivity]]: An operation <math>*</math> is ''left-distributive'' with respect to another operation <math>+</math> if <math display = block>x*(y+z)=(x*y)+(x*z) </math> for every {{mvar|x}}, {{mvar|y}} and {{mvar|z}} in the algebraic structure (the second operation is denoted here as <math>+</math>, because the second operation is addition in many common examples).
;[[Right distributivity]]: An operation <math>*</math> is ''right-distributive'' with respect to another operation <math>+</math> if <math display = block>(y+z)*x=(y*x)+(z*x) </math> for every {{mvar|x}}, {{mvar|y}} and {{mvar|z}} in the algebraic structure.
;[[Distributivity]]: An operation <math>*</math> is ''distributive'' with respect to another operation <math>+</math> if it is both left-distributive and right-distributive. If the operation <math>*</math> is commutative, left and right distributivity are both equivalent to distributivity.