Nov pristop k ohranjevalcem komutativnosti

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.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