| 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:
|
http://hdl.handle.net/10338.dmlcz/119416 |
| . |
| 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 rings.in: 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 |
| . |
