K-algebra

K-monoid

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

1. As an K-algebra 𝑇 which is unital and associative;
2. As a ring 𝑇 equipped with a homomorphism 𝑅 →Z⁡(𝑇) into its centre.

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

See also

• K-comonoid

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