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Linear algebra in lattices, the Fitting lemma

Jeno Szigeti
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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.

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Jeno Szigeti. 2007-03-09. Linear algebra in lattices, the Fitting lemma. https://arxiv.org/abs/math/0703253

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