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Title:Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)
Authors:Orel, Marko (Author)
Kuzma, Bojan (Author)
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:A complete classification of additive rank-one nonincreasing maps on hermitian matrices over Galois field ▫$GF(2^2)$▫ is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.
Keywords:mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Year of publishing:2009
Number of pages:str. 482-499
Numbering:Vol. 18
COBISS_ID:15240793 Link is opened in a new window
Categories:Document is not linked to any category.
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Secondary language

Title:Aditivne preslikave, ki ne povečujejo ranga ena na hermitskih matrikah nad obsegom GF(2[sup]2)
Abstract:Klasificirane so vse aditivne preslikave, ki ne povečujejo ranga ena na hermitskih matrikah s koeficienti iz obsega ▫$GF(2^2)$▫. Ta obseg je poseben in ni bil obravnavan v predhodnem članku. Nekatere znane aplikacije, kot je klasifikacija vseh aditivnih preslikav, ki ohranjajo aditivnost ranga, so posplošene na poljuben komutativen obseg. Klasificirane so tudi vse aditivne preslikave, ki ohranjajo kardinalnost hermitskih varietet.
Keywords:matematika, linearna algebra, aditivni ohranjevalci, hermitske matrike, rang, Galoisevi obsegi, šibki homomorfizmi grafov


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