Ideal theory in $f$-algebras
Ideal theory in $f$-algebras
The paper deals mainly with the theory of algebra ideals and order ideals in $f$-algebras. Necessary and sufficient conditions are established for an algebra ideal to be prime, semiprime or idempotent. In a uniformly complete $f$-algebra with unit element every algebra ideal is an order ideal iff the $f$-algebra is …