2 problems

Let $S$ be a finite commutative semigroup, let $K$ be a field, and let $\Gamma(H_a)$ denote the group associated with the $\mathcal H$-class of $a$. Write … Here $\bar a$ is the im…

Let $B$ be the affine semigroup under consideration, let $B_A$ denote its simplicial subsemigroup, and let $\sim$ be the equivalence relation on $B$. For $x,y\in B$, define … For…