Abstract
In this paper we study a class of commutative nonassociative algebras which includes those special Jordan algebras which arise as the set of all elements fixed by an involution in a primitive ring with nonzero socle and with centralizer which is a field of characteristic not 2. Perhaps the most unusual feature of our approach is that we do not assume that our algebras satisfy any identity, but only that enough primitive idempotents exist satisfying certain properties that follow from the Jordan identity. (For an introduction to the standard theory, see [6].) We also need an axiom which insures that the discrete topology (Jacobson’s finite topology) will suffice. More specifically, we assume that the following four axioms on idempotents hold in our algebra A over the field @ (A will be assumed to be commutative and of characteristic not 2 hereafter):
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
