Difference between revisions of "Multiary semigroup"

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(Created page with "==Definition== A '''multiary semigroup''', also called a '''polyadic semigroup''', is a <math>n</math>-ary semigroup for some <math>n \ge 2</math>. Note that the <math>n = 2<...")
 
 
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A <math>n</math>-ary semigroup is defined as a set <math>G</math> with a <math>n</math>-ary operation, i.e., a map <math>f: G^n \to G</math> such that all different ways of associating expressions involving the <math>n</math>-ary operation <math>f</math> yield equivalent results. Note that this boils down to checking that all the <math>n</math> distinct possible ways of associating an expression of length <math>2n - 1</math> give the same answer.
 
A <math>n</math>-ary semigroup is defined as a set <math>G</math> with a <math>n</math>-ary operation, i.e., a map <math>f: G^n \to G</math> such that all different ways of associating expressions involving the <math>n</math>-ary operation <math>f</math> yield equivalent results. Note that this boils down to checking that all the <math>n</math> distinct possible ways of associating an expression of length <math>2n - 1</math> give the same answer.
 
  
 
==Related notions==
 
==Related notions==

Latest revision as of 01:16, 19 June 2012

Definition

A multiary semigroup, also called a polyadic semigroup, is a n-ary semigroup for some n \ge 2. Note that the n = 2 case corresponds to the usual notion of semigroup.

A n-ary semigroup is defined as a set G with a n-ary operation, i.e., a map f: G^n \to G such that all different ways of associating expressions involving the n-ary operation f yield equivalent results. Note that this boils down to checking that all the n distinct possible ways of associating an expression of length 2n - 1 give the same answer.

Related notions