Abstract
Algebras of commutative languages consist of all subsets of a free commutative monoid over a given alphabet Σ, and they are endowed with the operations of union, complex multiplication, Kleene iteration (submonoid generation), and the empty set and the set whose unique element is the unit of the free monoid, as constants. There is a well-known equational axiomatization for these algebras. However, any such axiomatization is necessarily infinite. Now, by removing the operation of union (addition) from the described algebras, the corresponding equational theory reduces to the collection of those equations which contain no symbols of addition. We supply a nontrivial list of equational axioms for the so obtained equational theory, and prove that it has no finite equational base, too.
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