Dimension of Crystalline Graded Rings
Tim Neijens, Fred Van Oystaeyen
TL;DR
This paper calculates the global dimension of Crystalline Graded Rings, providing insights into their structural properties and conditions for semiprimeness, with additional discussion on Krull-dimension.
Contribution
It introduces the calculation of the global dimension for Crystalline Graded Rings, extending understanding of their algebraic properties.
Findings
Global dimension of Crystalline Graded Rings is determined.
A condition for these rings to be semiprime is established.
Discussion on Krull-dimension of these rings is included.
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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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra