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.
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