On the membership problem for pseudovarieties of commutative semigroups
The author shows that every pseudovariety of finite commutative semigroups admits a finite basis of pseudoidentities. On the other hand, he exhibits an example of a permutative pseudovariety without finite basis of pseudoidentities. He proves also that a pseudovariety of commutative semigroups has the membership problem decidable in polynomial time if and only if it admits a finite basis of pseudoidentities verifiable in polynomial time.
pseudovariety of finite commutative semigroups
scientific article; zbMATH DE number 4202593
scientific article