  This article is devoted to the investigation of $B^*$-algebras, dual and
annihilator ultranormed algebras. Their structure is studied in the paper.
Extensions of algebras and fields are considered and using them core radicals
and radicals are investigated. Moreover, for this purpose also $*$-algebras and
finely regular algebras are studied. Relations with operator theory and
realizations of these algebras by operator algebras are outlined.
