Finite Topologies and Their Applications in Linear Algebra

Using finite topologies defined on the algebra of linear operators, we investigate centralizers and double centralizers of locally algebraic linear operators. In particular, for an arbitrary locally algebraic operator , we establish the conditions under which the equality is fulfilled and, in the ca...

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Veröffentlicht in:Russian mathematics 2023, Vol.67 (1), p.74-81
Hauptverfasser: Abyzov, A. N., Maklakov, A. D.
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description Using finite topologies defined on the algebra of linear operators, we investigate centralizers and double centralizers of locally algebraic linear operators. In particular, for an arbitrary locally algebraic operator , we establish the conditions under which the equality is fulfilled and, in the case of an algebraically closed field, we describe minimal locally algebraic linear operators. We have studied automorphisms of dense in finite topology subrings of the rings of endomorphisms of free modules over projectively free rings.
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subjects Automorphisms
Linear algebra
Linear operators
Mathematics
Mathematics and Statistics
Oil field equipment
Operators (mathematics)
Rings (mathematics)
Topology
title Finite Topologies and Their Applications in Linear Algebra
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