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full affine semigroups; partially ordered abelian groups; semilocal rings; direct sum decompositions
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 $\text{\rm K}_0(R)$ for a semilocal ring $R$.
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[2] Facchini A.: Module theory. Endomorphism rings and direct sum decompositions in some classes of modules. Progress in Mathematics 197, Birkhäuser, 1998. MR 1634015 | Zbl 0930.16001
[3] Facchini A., Herbera D.: $K_0$ of a semilocal ring. J. Algebra 225 1 (2000), 47-69. MR 1743650 | Zbl 0955.13006
[4] Facchini A., Herbera D.: Projective modules over semilocal rings. in: D.V. Huynh (ed.) et al., Algebra and its Applications: Proceedings of the International Conference, Contemp. Math. 259, 2000, 181-198. MR 1778501 | Zbl 0981.16003
[5] Goodearl K.R.: Partially ordered abelian groups with interpolation. Mathematical Surveys and Monographs no. 20, Amer. Math. Soc., 1986. MR 0845783 | Zbl 0589.06008
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