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semimodular lattice; Goldie dimension; hollow dimension; Kurosh-Ore dimension
The aim of this paper is to present relations between Goldie, hollow and Kurosh-Ore dimensions of semimodular lattices. Relations between Goldie and Kurosh-Ore dimensions of modular lattices were studied by Grzeszczuk, Okiński and Puczyłowski.
[1] P.  Grzeszczuk and E. R.  Puczyłowski: On Goldie and dual Goldie dimensions. J.  Pure Appl. Algebra 31 (1984), 47–54. DOI 10.1016/0022-4049(84)90075-6 | MR 0738204
[2] P.  Grzeszczuk and E. R.  Puczyłowski: Goldie dimension and chain conditions for modular lattices with finite group actions. Canad. Math. Bull. 29 (1986), 274–280. DOI 10.4153/CMB-1986-042-9 | MR 0846704
[3] P.  Grzeszczuk, J.  Okiński and E. R.  Puczyłowski: Relations between some dimensions of modular lattices. Comm. Algebra 17 (1989), 1723–1737. DOI 10.1080/00927878908823816 | MR 1006522
[4] M.  Stern: Semimodular Lattices: Theory and Applications. University Press, Cambridge, 1999. MR 1695504 | Zbl 0957.06008
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