| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4588496 | Journal of Algebra | 2007 | 16 Pages |
Abstract
We show that the existence of a nontrivial proper ideal in a commutative ring with identity which is not a field is equivalent to WKL0 over RCA0, and that the existence of a nontrivial proper finitely generated ideal in a commutative ring with identity which is not a field is equivalent to ACA0 over RCA0. We also prove that there are computable commutative rings with identity where the nilradical is -complete, and the Jacobson radical is -complete, respectively.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
