ON THE MAXIMAL CARDINALITY OF CHAINS OF INTERMEDIATE RINGS
ON THE MAXIMAL CARDINALITY OF CHAINS OF INTERMEDIATE RINGS
All rings considered are commutative with 1 and all subrings are unital. If R ⊆ T are rings such that T is a finitely generated R-module, R is not a total quotient ring and (R : T) = 0, then there exists a denumerable chain of R-subalgebras of T. The rings having only finite chains of subrings are shown to be the same as the recently classified rings having only finitely many subrings.
Keywords:
Commutative ring, ring extension, subalgebra, chain, cardinality, determinant, FIP property, FSP property, integrality, greatest common divisor, pullback singly generated ring, integral domain, total quotient ring,
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- Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, U.S.A. e-mail: dobbs@math.utk.edu
- Gabriel Picavet and Martine Picavet-L’Hermitte Laboratoire de Math´ematiques Pures Universit´e Blaise Pascal Aubi`ere Cedex, France e-mails: Gabriel.Picavet@math.univ-bpclermont.fr Martine.Picavet@math.univ-bpclermont.fr
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI
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