Pavel P\v r\'\i hoda Bases of minimal elements of some partially ordered free abelian groups

Comment.Math.Univ.Carolinae 44,4 (2003) 623-628.

Abstract:In the present paper, we will show that the set of minimal elements of a full affine semigroup $A\hookrightarrow \Bbb N^k_0$ contains a free basis of the group generated by $A$ in $\Bbb Z^k$. This will be applied to the study of the group $\text {K}_0(R)$ for a semilocal ring $R$.

Keywords: full affine semigroups, partially ordered abelian groups, semilocal rings, direct sum decompositions
AMS Subject Classification: 16D70, 20M14