-algebra

-monoid

Let be a commutative ring. An -monoid is a monoid in the category . More concretely, an -monoid can be viewed in two equivalent ways: #m/def/calg

1. As an -algebra which is unital and associative;
2. As a ring equipped with a homomorphism into its centre.

This is of course a strenthening of -semigroup. It follows every ring is a -monoid in a unique way.

See also

• -comonoid

#state/tidy | #lang/en | #SemBr