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Let R ⊂ T be (commutative integral) domains, with corresponding quotient fields K ⊂ L. If R ≠ K, then there exists a denumerable chain of R-subalgebras of T. Examples show that the assertion fails if one deletes either of the assumptions that R ≠ K or K ≠ L or strengthens the “denumerable” part of the conclusion. A partial generalization is given for rings with nontrivial zero-divisors.
2000 Mathematics Subject Classification:
Communicated by I. Swanson.
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