monoid theory in algebra:
An idempotent monoid is a monoid which is idempotent in the sense that for all in the monoid.
By definition, every idempotent monoid is a unital band.
A semilattice (in this article, we mean semilattices with identity) is the same thing as a commutative idempotent monoid.
An idempotent semiring is a semiring whose addition operation is an idempotent monoid.
A Boolean ring is a ring whose multiplication operation is an idempotent monoid.
A multiplicatively idempotent rig is a rig whose multiplication operation is an idempotent monoid.
The concept of an idempotent monoid can be internalized in any monoidal category with diagonals; see idempotent monoid object for more details.
Last revised on June 14, 2025 at 08:48:44. See the history of this page for a list of all contributions to it.