Regnath, H. and Seibert, Gerhard (1998) Frobenius functors and invariant factors. COMMUNICATIONS IN ALGEBRA, 26 (6). pp. 1757-1768. ISSN 0092-7872, 1532-4125
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Let (R, m) be a noetherian local ring of prime characteristic and F-R(_) be the Frobeuius functor. We will show that for all finite R-modules M there is an n is an element of IN (depending on M) such that the fundamental theorem for modules over principal domains holds for F-R(n)(M), i.e. there are r, s is an element of IN and elements a(1),...,a(s) is an element of m \ {0} with (a(1)) superset of ... superset of (a(s)) and F-R(n)(M) congruent to R-tau + R/(a(1)) + ... + R/(a(s)) if and only if R is geometrically unibranch in the sense of Grothendieck [2] and dim R less than or equal to 1. For example, R is geometrically unibranch, if it is complete and R/m is an algebraically closed field.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Feb 2023 11:12 |
| Last Modified: | 28 Feb 2023 11:12 |
| URI: | https://pred.uni-regensburg.de/id/eprint/50181 |
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