Ring extensions and essential monomorphisms

Würfel, Tilmann

doi:10.1090/S0002-9939-1978-0482574-6

Ring extensions and essential monomorphisms
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Proc. Amer. Math. Soc. 69 (1978), 1-7 Request permission

Abstract:

We study pairs of rings $R \subset S$ such that $\operatorname {Hom}_R(S, - ):R - \operatorname {Mod} \to S - \operatorname {Mod}$ preserves essential monomorphisms. We obtain a complete characterization of such a pair in case S is a torsion-free algebra over a Noetherian domain $R \ne \mathrm {Quot}(R)$; S is then a left ideally finite R-algebra. The rings R such that every ring extension $R \subset S$ satisfies the above condition are subdirect sums of certain Artinian rings. Furthermore, we study a generalization of trivial ring extensions and show that the center of a semi-Artinian ring is again semi-Artinian.

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