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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The unity in rings with Gabriel and Krull dimension


Author: F. Hansen
Journal: Proc. Amer. Math. Soc. 55 (1976), 281-286
MSC: Primary 16A46
DOI: https://doi.org/10.1090/S0002-9939-1976-0401834-6
MathSciNet review: 0401834
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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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DOI: https://doi.org/10.1090/S0002-9939-1976-0401834-6
Keywords: Right unity, unity, Krull dimension, Gabriel dimension, simple ring, Goldie ring, maximum condition for annihilating right ideals, finite uniform dimension
Article copyright: © Copyright 1976 American Mathematical Society