Commutativity preserving maps revisited

Abstract

K. I. Beidar in Y.-F. Lin sta dokazala, da je pod določenimi pogoji linearni ohranjevalec komutativnosti med (jordanskima) algebrama ▫$\mathcal{A}$▫ in ▫$\mathcal{Q}$▫ standardne oblike, razen če preslikava določeno (običajno "veliko") podmnožico ▫$\mathcal{A}$▫ slika v center ▫$\mathcal{Q}$▫. Ta rezultat dopolnimo z ugotovitvijo, da ta množica pogosto vsebuje neničelni ideal. To nam omogoči podati dokončen rezultat o ohranjevalcih komutativnosti na enostavnih kolobarjih, kot tudi na prakolobarjih, če predpostavimo ohranjanje komutativnosti v obeh smereh.

Keywords

matematika;algebra;ohranjevalec komutativnosti;funkcijska identiteta;jordanski kolobar;prakolobar;involucija;mathematics;functional identity;commutativity preserving map;Jordan ring;prime ring;involution;

Data

Language:	English
Year of publishing:	2007
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552
COBISS:	14551129
ISSN:	0021-2172
Views:	43
Downloads:	3
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Nov pristop k ohranjevalcem komutativnosti
Secondary abstract:	K. I. Beidar and Y.-F. Lin have recently showed that under appropriate conditions a commutativity preserving map between (Jordan) algebras ▫$\mathcal{A}$▫ and ▫$\mathcal{Q}$▫ is of a standard form, unless it sends a certain subset of ▫$\mathcal{A}$▫, which one could describe (unless ▫$\mathcal{A}$▫ is very special) as a "large" one, into the center of ▫$\mathcal{Q}$▫. We give a supplement to this statement by showing that this set often contains a nonzero ideal. In particular this makes it possible for us to give the definitive description of commutativity preservers in simple rings, as well as in prime rings provided that the map in question preserves commutativity in both directions.
Secondary keywords:	matematika;algebra;ohranjevalec komutativnosti;funkcijska identiteta;jordanski kolobar;prakolobar;involucija;
Type (COBISS):	Not categorized
Pages:	str. 317-334
Volume:	ǂVol. ǂ162
Issue:	ǂno. ǂ1
Chronology:	2007
ID:	1473450