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Chain Conditions for Modular Lattices with Finite Group Actions

Published online by Cambridge University Press:  20 November 2018

Joe W. Fisher
Joe W. Fisher*
Affiliation:
University of Cincinnati, Cincinnati, Ohio
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 558 - 564
Copyright
Copyright © Canadian Mathematical Society 1979

References

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