Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-3, author = {Matej Bre\v sar and Ajda Fo\v sner and Maja Fo\v sner}, title = {A Kleinecke-Shirokov type condition with Jordan automorphisms}, journal = {Studia Mathematica}, volume = {147}, year = {2001}, pages = {237-242}, zbl = {1058.46506}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-3} }
Matej Brešar; Ajda Fošner; Maja Fošner. A Kleinecke-Shirokov type condition with Jordan automorphisms. Studia Mathematica, Tome 147 (2001) pp. 237-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-3/