## 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

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