20.500.12556/RUP-7730 Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2) Aditivne preslikave, ki ne povečujejo ranga ena na hermitskih matrikah nad obsegom GF(2[sup]2) 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. 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. mathematics linear algebra additive preserver hermitian matrices rank Galois field weak homomorphism of a graph matematika linearna algebra aditivni ohranjevalci hermitske matrike rang Galoisevi obsegi šibki homomorfizmi grafov true true false Angleški jezik Slovenski jezik Delo ni kategorizirano 2016-04-08 16:46:43 2017-04-03 08:12:32 2024-03-01 13:33:24 0000-00-00 00:00:00 2009 0 0 str. 482-499 Vol. 18 2009 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1081-3810 512.643 13706329 15240793 http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol18_pp482-499.pdf 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=7730 Inštitut Andrej Marušič 0 0 0