The unity in rings with Gabriel and Krull dimension

Hansen, F.

doi:10.1090/S0002-9939-1976-0401834-6

The unity in rings with Gabriel and Krull dimension
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Proc. Amer. Math. Soc. 55 (1976), 281-286 Request permission

Abstract:

The main result is that all rings with right Krull dimension and divisible torsion free additive group have a right identity. Furthermore it will be proved that a simple ring with characteristic $0$, right Gabriel dimension $\leqslant 2$ and finite right uniform dimension has a unity. This is false for higher Gabriel dimensions, as demonstrated by a counterexample. A similar construction gives an example for a ring with unity and Gabriel dimension, but without Krull dimension, all factor rings having finite uniform dimension.

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