Jordan ideals revisited.
The authors approach the study of Jordan ideals in rings by using the identity \([[a,b],c]=a\circ(b\circ c)-b\circ(a\circ c)\). This provides a fairly simple way to recapture the classical results that relate Jordan ideals to ideals. The approach here puts these known results is a more general setting applicable to certain rings of operators. The authors' methods exend to graded algebras with an anti-symmetric bicharacter, giving Jordan color algebras. Here they obtain recent results on \(\varepsilon\)-Jordan ideals, analogous to the results in the classical case, but again in a more general setting. When the rings, graded or not, have involution, then the authors recover known results on the Jordan ideals of the set of symmetric elements.
scientific article; zbMATH DE number 2175899