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 |
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creator | Abyzov, A. N. Maklakov, A. D. |
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. |
doi_str_mv | 10.3103/S1066369X23010012 |
format | Article |
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, 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.</description><identifier>ISSN: 1066-369X</identifier><identifier>EISSN: 1934-810X</identifier><identifier>DOI: 10.3103/S1066369X23010012</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Automorphisms ; Linear algebra ; Linear operators ; Mathematics ; Mathematics and Statistics ; Oil field equipment ; Operators (mathematics) ; Rings (mathematics) ; Topology</subject><ispartof>Russian mathematics, 2023, Vol.67 (1), p.74-81</ispartof><rights>Allerton Press, Inc. 2023. ISSN 1066-369X, Russian Mathematics, 2023, Vol. 67, No. 1, pp. 74–81. © Allerton Press, Inc., 2023. Russian Text © The Author(s), 2023, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, No. 1, pp. 87–96.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c198t-c5235be91b75f43d3b3dbd9343caa4adc080088455632665d965e0f709545d253</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.3103/S1066369X23010012$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.3103/S1066369X23010012$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Abyzov, A. N.</creatorcontrib><creatorcontrib>Maklakov, A. D.</creatorcontrib><title>Finite Topologies and Their Applications in Linear Algebra</title><title>Russian mathematics</title><addtitle>Russ Math</addtitle><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
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, 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.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.3103/S1066369X23010012</doi><tpages>8</tpages></addata></record> |
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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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