We present several naturally defined ฯ-ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set-theoretic properties of such ฯ-ideals.
The Complexity of Frobenius Powers of Ideals
โ Scribed by Mordechai Katzman
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 205 KB
- Volume
- 203
- Category
- Article
- ISSN
- 0021-8693
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๐ SIMILAR VOLUMES
Let K be a field of characteristic different from 2. In the algebraic theory of ลฝ . quadratic forms, one studies the Witt ring W K of equivalence classes of non-den ลฝ . generate quadratic forms. The Witt ring has a filtration given by the powers I K ลฝ . n ลฝ . of the fundamental ideal I K of even-dim
Given a local ring R and n ideals whose sum is primary to the maximal ideal of ลฝ . R, one may define a function which takes an n-tuple of exponents a , . . . , a to 0 1 2 1 2 although this has not yet proved possible. We are, however, able to establish certain properties of the functions f in some g