Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T06:20:13.534Z Has data issue: false hasContentIssue false
  • English
  • Français

LINEAR PROPERTIES OF GOLDIE DIMENSION OF MODULES AND MODULAR LATTICES

Published online by Cambridge University Press:  24 June 2010

EDMUND R. PUCZYŁOWSKI
EDMUND R. PUCZYŁOWSKI*
Affiliation:
Institute of Mathematics, University of Warsaw, 02–097 Warsaw, Banacha 2, Poland e-mail: edmundp@mimuw.edu.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We survey some old and recent results concerning the Goldie dimension of modules and modular lattices and its properties which are counterparts of properties of the dimension of linear spaces.

Keywords

Primary 16P6006C05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue A: Rings and Modules in Honour of Patrick F. Smith's 65th Birthday , July 2010 , pp. 139 - 150
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Albu, T., Iosif, M. and Teply, M. L., Dual Krull dimension and quotient finite dimensionality, J. Algebra 284 (2005), 52–79.CrossRefGoogle Scholar
2.Albu, T. and Smith, P. F., Localization of modular lattices, Krull dimension, and the Hopkins–Levitzki theorem II. Comm. Algebra 25 (1997), 1111–1128.CrossRefGoogle Scholar
3.Anderson, F. W. and Fuller, K. R., Rings and categories of modules (Springer Verlag, New York, 1974).CrossRefGoogle Scholar
4.Camillo, V. and Zelmanowitz, J., On the dimension of a sum of modules, Comm. Algebra 6 (1978), 345–352.CrossRefGoogle Scholar
5.Camillo, V. P. and Zelmanowitz, J. M., Dimension modules, Pacific J. Math. 91 (1980), 249–261.CrossRefGoogle Scholar
6.Dawson, J. E., Independence spaces and uniform modules, Europ. J. Comb. 6 (1985), 29–36.CrossRefGoogle Scholar
7.Dawson, J. E., Independence structures on the submodules of a module, Europ. J. Comb. 6 (1985), 37–44.CrossRefGoogle Scholar
8.Dauns, J. and Fuchs, L., Infinite Goldie dimension, J. Algebra 115 (1988), 297–302.CrossRefGoogle Scholar
9.Domagalska, P. and Puczyłowski, E. R., Dimension modules and modular lattices, preprint.Google Scholar
10.Fleury, P., A note on dualizing Goldie dimension, Canad. Math. Bull. 17 (1974), 511–517.CrossRefGoogle Scholar
11.Grätzer, G., General lattice theory (Birkhäuser Verlag, Basel, Switzerland, 1978).CrossRefGoogle Scholar
12.Grzeszczuk, P. and Puczyłowski, E. R., On Goldie and dual Goldie dimensions, J. Pure Appl. Algebra 31 (1984), 47–54.CrossRefGoogle Scholar
13.Grzeszczuk, P. and Puczyłowski, E. R., On infinite Goldie dimension of modular lattices and modules, J. Pure and Appl. Algebra 35 (1985), 151–155.CrossRefGoogle Scholar
14.Grzeszczuk, P., Okniński, J. and Puczyłowski, E. R., Relations between some dimensions of modular lattices, Comm. Algebra 17 (1989), 1723–1737.CrossRefGoogle Scholar
15.Grzeszczuk, P. and Puczyłowski, E. R., Gabriel and Krull dimensions of modules over rings graded by finite groups, Proc. Amer. Math. Soc. 105 (1989), 17–24.CrossRefGoogle Scholar
16.Krempa, J., On lattices, modules and groups with many uniform elements, Algebra Discrete Math. 1 (2004), 75–86.Google Scholar
17.Krempa, J. and Terlikowska-Osłowska, B., On uniform dimension of lattices, Contrib. Gen. Algebra 9 (Linz, 1994), 219–230 (Holder-Pichler-Tempsky, Vienna, 1995).Google Scholar
18.Puczylowski, E. R., On some dimensions of modular lattices and matroids, in International symposium on ring theory (Kyongju, 1999), 303–312 (Trends Math., Birkhauser Boston, Boston, MA, 2001).Google Scholar
19.Puczyłowski, E. R., A linear property of Goldie dimension of modules and modular lattices, submitted.Google Scholar
20.Welsh, D. J. A., Matroid theory (Academic Press, London, 1976).Google Scholar
21.Varadarajan, K., Dual Goldie dimension, Comm. Algebra 7 (1979), 565–610.CrossRefGoogle Scholar
22.del Valle, A., Goldie dimension of a sum of modules, Comm. Algebra 22 (1994), 1257–1269.CrossRefGoogle Scholar
23.Zolotarev, A. P., Balanced lattices and Goldie numbers in balanced lattices. Sibirsk. Mat. Zh. (Russian) 35 (1994), 602–611; translation in Siberian Math. J. 35 (1994), 539–546.Google Scholar
24.Zolotarev, A. P., On the interconnection among Helly, Radon and Caratheodory numbers in lattices with a balanced skeleton. Izv. Vyssh. Uchebn. Zaved. Mat. (11) (1992), 17–22 (1993); translation in Russian Math. (Iz. VUZ) 36 (11) (1992), 15–20.Google Scholar