Abstract
Let R be a ring and let r be an hereditary torsion theory such that R has the descending chain condition on r-closed left ideals. Let {P 1, P 2 ·, P n } be a link closed set of r-closed prime ideals and C be a left reversible left Ore set in \(C\left( {\bigcap\limits_{i = 1}^n {P_i } } \right)\). If C −1 R is left artinian, then r can be modified to another torsion theory σ such that R has DCC on σ-closed left ideals and the primitive ideals of C −1 R are precisely localizations of the σ-closed prime ideals of R. As an application, new information about localization at sets of minimal primes in rings with left Krull dimension and in Noetherian rings is obtained. The condition that the primitive ideals of C −1 R are precisely {C −1 P 1, C −1 P 2, ·, C −1 P n } is also studied.
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Teply, M.L., Torrecillas, B. (1990). Primitive ideals of nice Ore localizations. In: Jain, S.K., López-Permouth, S.R. (eds) Non-Commutative Ring Theory. Lecture Notes in Mathematics, vol 1448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091251
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DOI: https://doi.org/10.1007/BFb0091251
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