Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)

Marko Orel (Author), Bojan Kuzma (Author)

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;mathematics;linear algebra;additive preserver;hermitian matrices;rank;Galois field;weak homomorphism of a graph;

Data

Language:	English
Year of publishing:	2009
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	512.643
COBISS:	15240793
ISSN:	1081-3810
Views:	44
Downloads:	6
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Aditivne preslikave, ki ne povečujejo ranga ena na hermitskih matrikah nad obsegom GF(2[sup]2)
Secondary 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.
Secondary keywords:	matematika;linearna algebra;aditivni ohranjevalci;hermitske matrike;rang;Galoisevi obsegi;šibki homomorfizmi grafov;
Type (COBISS):	Not categorized
Pages:	str. 482-499
Issue:	Vol. 18
Chronology:	2009
ID:	1474414