Linear algebra in lattices, the Fitting lemma
Rings and Algebras
2007-05-23 v1 General Mathematics
Abstract
Lattice theoretical generalizations of some classical linear algebra results are formulated. A vector space is replaced by its subspace lattice and a linear map is replaced by the induced lattice map. This map is a complete join homomorphism and satisfies some additional natural conditions. The object of our study is a pair consisting of a complete lattice and one of its complete join endomorphisms. We prove the Fitting lemma for such a pair.
Cite
@article{arxiv.math/0703253,
title = {Linear algebra in lattices, the Fitting lemma},
author = {Jeno Szigeti},
journal= {arXiv preprint arXiv:math/0703253},
year = {2007}
}
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6 pages