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arXiv · 0903.4645

Dimension of Crystalline Graded Rings

Tim Neijens·Fred Van Oystaeyen
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Abstract

The global dimension of a ring governs many useful abilities. For example, it is semi-simple if the global dimension is 0, hereditary if it is 1 and so on. We will calculate the global dimension of a Crystalline Graded Ring, as defined in the paper by E. Nauwelaerts and F. Van Oystaeyen, Introducing Crystalline Graded Algebras, Algebras and Representation Theory vol 11(2008), no. 2, 133--148.. We will apply this to derive a condition for the Crystalline Graded Ring to be semiprime. In the last section, we give a little bit of attention to the Krull-dimension.

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Tim Neijens, Fred Van Oystaeyen. 2009-03-26. Dimension of Crystalline Graded Rings. https://arxiv.org/abs/0903.4645

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