Ideal arithmetic in Noetherian PI rings
If R is a commutative noetherian domain then every ideal of R is a product of prime ideals if and only if every non-zero ideal of R is invertible. In this paper, the authors study noncommutative versions of this result. A (noncommutative) ring R is a Dedekind prime ring if it is noetherian, hereditary and every non-zero ideal is invertible. The authors prove that a prime noetherian PI ring R is a Dedekind prime ring if and only if every ideal is a product of maximal ideals and that R is then a finite module over its centre which is a Dedekind domain. A key point is that a one-sided invertible ideal is both right and left localisable - this depends on a recent symmetry result of \textit{A. Braun} and \textit{R. B. Warfield} jun. [J. Algebra 118, 322-335 (1988; Zbl 0658.16008)].
scientific article; zbMATH DE number 4097569
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