Ideals in Computable Rings
نویسندگان
چکیده
We show that the existence of a nontrivial proper ideal in a commutative ring with identity which is not a eld is equivalent to WKL0 over RCA0, and that the existence of a nontrivial proper nitely generated ideal in a commutative ring with identity which is not a eld is equivalent to ACA0 over RCA0. We also prove that there are computable commutative rings with identity where the nilradical is 0 1 -complete, and the Jacobson radical is 0 2 -complete, respectively.
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