# Bases of minimal elements of some partially ordered free abelian groups

Commentationes Mathematicae Universitatis Carolinae (2003)

- Volume: 44, Issue: 4, page 623-628
- ISSN: 0010-2628

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topPříhoda, Pavel. "Bases of minimal elements of some partially ordered free abelian groups." Commentationes Mathematicae Universitatis Carolinae 44.4 (2003): 623-628. <http://eudml.org/doc/249169>.

@article{Příhoda2003,

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

author = {Příhoda, Pavel},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {full affine semigroups; partially ordered abelian groups; semilocal rings; direct sum decompositions; full affine semigroups; partially ordered Abelian groups; semilocal rings; direct sum decompositions; finitely generated projective modules},

language = {eng},

number = {4},

pages = {623-628},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Bases of minimal elements of some partially ordered free abelian groups},

url = {http://eudml.org/doc/249169},

volume = {44},

year = {2003},

}

TY - JOUR

AU - Příhoda, Pavel

TI - Bases of minimal elements of some partially ordered free abelian groups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2003

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 44

IS - 4

SP - 623

EP - 628

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

LA - eng

KW - full affine semigroups; partially ordered abelian groups; semilocal rings; direct sum decompositions; full affine semigroups; partially ordered Abelian groups; semilocal rings; direct sum decompositions; finitely generated projective modules

UR - http://eudml.org/doc/249169

ER -

## References

top- Bruns W., Herzog J., Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, 1993. Zbl0909.13005MR1251956
- Facchini A., Module theory. Endomorphism rings and direct sum decompositions in some classes of modules, Progress in Mathematics 197, Birkhäuser, 1998. Zbl0930.16001MR1634015
- Facchini A., Herbera D., ${K}_{0}$ of a semilocal ring, J. Algebra 225 1 (2000), 47-69. (2000) Zbl0955.13006MR1743650
- 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. Zbl0981.16003MR1778501
- Goodearl K.R., Partially ordered abelian groups with interpolation, Mathematical Surveys and Monographs no. 20, Amer. Math. Soc., 1986. Zbl0589.06008MR0845783

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