symmetric monoidal (∞,1)-category of spectra
monoid theory in algebra:
An absorption monoid or annihilation monoid is a monoid $(M,1,\cdot)$ that is also an absorption magma $(M,0)$.
A non-zero element $a \in M$ is a zero divisor if there exists a non-zero element $b \in M$ such that $a \cdot b = 0$.
The localization of an absorption monoid at $0$ is the trivial group. Because of this, the group completion of any absorption monoid is the trivial group. This is why one speaks of division monoids instead of groups in the context of absorption monoids, and in particular, why the additive identity element in any nontrivial field has no multiplicative inverse.
The extended natural numbers $(\bar{\mathbb{N}}, 0, +, \infty)$ are an absorption monoid.
Every integral monoid is an absorption monoid.
The multiplicative monoid of every rig is an absorption monoid.
Every join-semilattice with a top element and evety meet-semilattice with a bottom element is an absorption monoid.
Last revised on May 20, 2022 at 21:17:38. See the history of this page for a list of all contributions to it.