Definition
A (commutative) monoid \(S\) is said to be…
- …dull if \(S^* = S\), i.e. if \(S\) is a group
- …integral (or sometimes cancellative) if whenever \(a + c = b+c\) for \(a,b,c\in S\), \(a = b\).
- …\(u\)-integral if whenever \(a\in S\), \(u\in S^*\) and \(s + u = s\) then \(u = 0\).
- …sharp if \(S^* = \{0\}\), i.e. \(0\) is the only invertible element in \(S\)
See also toric monoid.