All Questions

Suppose I have a monoid $(M,\, \cdot,\, e)$ equipped with a monoid homomorphism $\textrm{length} : M \rightarrow \mathbb{N}_+$ into the monoid of natural numbers under addition where $e$ is the only ...

Do you know rings without involutions, but auto-anti-isomorphic (isomorphic to their opposite)? In that case, what is the minimal example? If a ring has an involution f, then f is an anti-automorphism;...

Let $H$ be a monoid, and denote by $H^\times$ and $\mathcal A(H)$, respectively, the set of units (or invertible elements) and the set of atoms (or irreducible elements) of $H$ (an element $a \in H$ ...