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Goldie Dimension and Chain Conditions for Modular Lattices with Finite Group Actions

Published online by Cambridge University Press:  20 November 2018

Piotr Grzeszczuk  and
Edmund R. Puczyłowski
Piotr Grzeszczuk
Affiliation:
Institute of Mathematics, University of WarsawBiałystok Division Akademicka 2 15-267 Białystok, Poland
Edmund R. Puczyłowski
Affiliation:
Institute of Mathematics, University of WarsawPKIN 00-901 Warsaw, Poland
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Abstract

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A relation between Goldie dimensions of a modular lattice L and its sublattice LG of fixed points under a finite group G of automorphisms of L is obtained. The method used also gives a relation between ACC (DCC) for L and for LG. The results obtained are applied to rings and modules.

Keywords

06C0516A72
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 274 - 280
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Grawley, P. and Dilworth, R. P., Algebraic Theorey of Lattices, Prentice-Hall, Englewood Cliffs, N.J., 1973.Google Scholar
2. Fisher, J., Chain conditions for modular lattices with finite group actions, Canad. J. of Math., 31 (1979), pp. 31–1979.Google Scholar
3. Grätzer, G., General Lattice Theorey, Birkhauser-Verlag, Basel, 1978.Google Scholar
4. Grzeszczuk, P. and Puczyłowski, E. R., On Goldie and dual Goldie dimensions, J. Pure Appl. Algebra, 31 (1984), pp. 47–54.Google Scholar
5. Grzeszczuk, P. and Puczyłowski, E. R., On infinite Goldie dimension of modular lattices and modules, J. Pure Appl. Algebra, 35 (1985), pp. 35–1985.Google Scholar
6. Kharchenko, V. K., Galois extensions and quotient rings, Algebra i Logika, 13 (1974), pp. 13—1974.(Russian).Google Scholar
7. Montgomery, S., Fixed rings of finite automorphism groups of associative rings, LNM 818, Springer Verlag, 1980.Google Scholar
8. Sarath, B. and Varadarajan, K., Dual Goldie dimension — II, Comm. in Algebra, 17 (1979), pp. 17–1979.Google Scholar
9. Van Oystaeyen, F., On Clifford systems and generalized crossed products, J. Algebra, 87 (1984), pp. 87–1984.Google Scholar
10. Varadarajan, K., Dual Goldie dimension, Comm. in Algebra, 7 (1979), pp. 7 — 1979.Google Scholar