Dimension of Crystalline Graded Rings

Details Dimension of Crystalline Graded Rings Dimension of Crystalline Graded Rings

2009-03-26

arxiv.org/abs/0903.4645v1

Mathematics

Rings and Algebras

Scientific paper

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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