R-algebra

-monoid

Let be a commutative ring. An -monoid is a monoid in the category [[Category of modules over a commutative ring|]]. More concretely, an -monoid can be viewed in two equivalent ways: calg

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

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

See also

• R-comonoid

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