Endomorphism monoids in varieties of commutative semigroups

Abstrakt

A concrete category is almost universal if its class of non-constant morphisms contains an isomorphic copy of every category of algebras as a full subcategory. This paper characterizes almost universal varieties of commutative semigroups.

As a consequence we obtain that for every infinite cardinal $\kappa$ there exists a commutative semigroup of cardinality $\kappa$ such that it has exactly two endomorphisms, the identity endomorphism and a single constant endomorphism.

Klíčová slova

• commutative semigroup
• commutative monoid
• almost universality