Krull dimension and reflexivity in some Noetherian rings

Haghany, A.; Sarath, B.

doi:10.1090/S0002-9939-1981-0619968-1

Krull dimension and reflexivity in some Noetherian rings
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by A. Haghany and B. Sarath PDF

Proc. Amer. Math. Soc. 83 (1981), 1-7 Request permission

Abstract:

In this paper we study Noetherian prime rings $R$ which satisfy the formula $\left | R \right | = \sup \{ \left | {{I^{* *}}/I} \right |:I$ is an essential left ideal of $R\} + 2$, where $|\;|$ denotes left Krull dimension. If further $Q/R$ is $\left | R \right | - 1$ unmixed, where $Q$ is the simple Artinian quotient ring of $R$, we characterize $R$ using torsion theories cogenerated by the injective hulls of $\left | R \right | - 1$ dimensional critical modules. Also equivalent statements are established, linking homological properties with dimension theory, for $R$-modules to be reflexive.

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