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Title: Bases of minimal elements of some partially ordered free abelian groups (English)
Author: Příhoda, Pavel
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 44
Issue: 4
Year: 2003
Pages: 623-628
Category: math
Summary: 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 $R$. (English)
Keyword: full affine semigroups
Keyword: partially ordered abelian groups
Keyword: semilocal rings
Keyword: direct sum decompositions
MSC: 06F20
MSC: 16D40
MSC: 16D70
MSC: 16E20
MSC: 20F60
MSC: 20M14
idZBL: Zbl 1101.16010
idMR: MR2062878
Date available: 2009-01-08T19:31:38Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Bruns W., Herzog J.: Cohen-Macaulay rings.Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, 1993. Zbl 0909.13005, MR 1251956
Reference: [2] Facchini A.: Module theory. Endomorphism rings and direct sum decompositions in some classes of modules.Progress in Mathematics 197, Birkhäuser, 1998. Zbl 0930.16001, MR 1634015
Reference: [3] Facchini A., Herbera D.: $K_0$ of a semilocal ring.J. Algebra 225 1 (2000), 47-69. Zbl 0955.13006, MR 1743650
Reference: [4] Facchini A., Herbera D.: Projective modules over semilocal D.V. Huynh (ed.) et al., Algebra and its Applications: Proceedings of the International Conference, Contemp. Math. 259, 2000, 181-198. Zbl 0981.16003, MR 1778501
Reference: [5] Goodearl K.R.: Partially ordered abelian groups with interpolation.Mathematical Surveys and Monographs no. 20, Amer. Math. Soc., 1986. Zbl 0589.06008, MR 0845783


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