## 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