  It has been established by Inoue that a complex locally C*-algebra with a
dense ideal posesses a bounded approximate identity which belonges to that
ideal. It has been shown by Fritzsche that if a unital complex locally
C*-algebra has an unbounded element then it also has a dense one-sided ideal.
In the present paper we obtain analogues of the aforementioned results of Inoue
and Fritzsche for real locally C*-algebras (projective limits of projective
families of real C*-algebras), and for locally JB-algebras (projective limits
of projective families of JB-algebras).
