Normalizing Extensions of Semiprime Rings (original) (raw)

Abstract. In this paper we study normalizing extensions of semiprime rings. For an extension S of R we construct the canonical torsion-free S∗, which is a normalizing extension of the symmetric ring of quotients Q of R. We extend results which are known for centralizing extensions and for normalizing bimodules to one-to-one correspondence between closed ideals. Finally we study prime ideals, non-singular prime ideals and (right) strongly prime ideals of intermediate extensions. MSC 2000: 16D20, 16D30, 16S20, 16S90