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Reduction Techniques for Strongly Graded Rings and Finite Representation Type

✍ Scribed by Jeremy Haefner

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 317 KB
Volume: 194
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7031

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✦ Synopsis

We present reduction techniques for studying the category of lattices over strongly graded orders. In particular, we apply these techniques in order to reduce the problem of classifying those strongly graded orders with finite representation type to the case where the coefficient ring is a maximal order in a division ring.

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For any pair n , k of positive integers we produce a strongly Z -graded ring R 2 such that the identity component R has invariant basis number while the 0 integers n, k and n , k having n F n and k ¬ k we produce a strongly Z -graded 2 Ž . ring R such that the basis-number type of R is n, k while t