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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Injective modules and localization in noncommutative Noetherian rings
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by Arun Vinayak Jategaonkar PDF
Trans. Amer. Math. Soc. 190 (1974), 109-123 Request permission

Abstract:

Let $\mathfrak {S}$ be a semiprime ideal in a right Noetherian ring R and $\mathcal {C}(\mathfrak {S}) = \{ c \in R|[c + \mathfrak {S}$ regular in $R/\mathfrak {S}\}$. We investigate the following two conditions: $({\text {A}})\;\mathcal {C}(\mathfrak {S})$ is a right Ore set in R. $({\text {B}})\;\mathcal {C}(\mathfrak {S})$ is a right Ore set in R and the right ideals of ${R_{\mathfrak {S}}}$, the classical right quotient ring of R w.r.t. $\mathcal {C}(\mathfrak {S})$ are closed in the $J({R_{\mathfrak {S}}})$-adic topology. The main results show that conditions (A) and (B) can be characterized in terms of the injective hull of the right R-module $R/\mathfrak {S}$. The J-adic completion of a semilocal right Noetherian ring is also considered.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 190 (1974), 109-123
  • MSC: Primary 16A08
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0349727-X
  • MathSciNet review: 0349727