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Concatenation
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==Algebraic properties== The strings over an alphabet, with the concatenation operation, form an [[associative property|associative]] algebraic structure called a [[free monoid]]. The [[identity element]] is the [[null string]]. Sets of strings with concatenation and [[Alternation (formal language theory)|alternation]] form a [[semiring]], with concatenation [[distributive property|distributing]] over alternation. The identity for alternation (the 0 element) is the [[empty set]] and identity for concatenation (the 1 element) is the set containing just the null string.
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