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- Title
Some more combinatorics results on Nagata Extensions.
- Authors
Picavet, Gabriel; Picavet-L'Hermitte, Martine
- Abstract
We show that the length of a ring extension R ⊆ S is preserved under the formation of the Nagata extension R(X) ⊆ S(X). A companion result holds for the Dobbs-Mullins invariant. D. Dobbs and the authors proved elsewhere that the cardinal number of the set [R, S] of subextensions of R ⊆ S is preserved under the formation of Nagata extension when |[R(X), S(X)]| is finite. We show that in the only pathological case, namely R ⊆ S is subintegral, then |[R, S]| is preserved if and only if it is either infinite or finite and R ⊆ S is arithmetic; that is, [R, S] is locally a chain. The last section gives properties of arithmetic extensions and their links with Prüfer extensions.
- Subjects
RING extensions (Algebra); COMBINATORICS; PRUFER rings
- Publication
Palestine Journal of Mathematics, 2016, Vol 5, p49
- ISSN
2219-5688
- Publication type
Article