Chain Conditions for Modular Lattices with Finite Group Actions
- 1 June 1979
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 31 (3) , 558-564
- https://doi.org/10.4153/cjm-1979-058-9
Abstract
This paper establishes the following combinatorial result concerning the automorphisms of a modular lattice.THEOREM. Let M be a modular lattice and let G be a finite subgroup of the automorphism group of M. If the sublattice, MG, of (common) fixed points (under G) satisfies any of a large class of chain conditions, then M satisfies the same chain condition. Some chain conditions in this class are the following: the ascending chain condition; the descending chain condition; Krull dimension; the property of having no uncountable chains, no chains order-isomorphic to the rational numbers; etc.Keywords
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