Elasticity of factorizations in R 0 + X R1 + … + X lRl [X]
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abstract
For an atomic domain R the elasticity ρ(R) is defined by ρ(R) = sup{m/n ¦ u1 … u m = v 1 … vn where ui, vi ∈ R are irreducible}. Let R 0 ⊂ … ⊂ R l be an ascending chain of domains which are finitely generated over ℤ and assume that R l is integral over R 0. Let X be an indeterminate. In this paper we characterize all domains D of the form D = R 0 + XR1 + … + XlRl[X] whose elasticity ρ(D) is finite.
The 2000 Mathematics Subject Classification is
11R27 13G05 13A05Preview
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References
- [1]D.D. Anderson (ed.), Factorization in Integral Domains, Lecture Notes in Pure and Appl. Math. 189, Marcel Dekker 1997.Google Scholar
- [2]D.F. Anderson, Elasticity of Factorizations in Integral Domains: A Survey, in [1], 1-29.Google Scholar
- [3]D.D. Anderson, D.F. Anderson, M. Zafrullah, Factorization in integral domains, J. Pure Appl. Algebra 69 (1990) 1–19.MathSciNetMATHCrossRefGoogle Scholar
- [4]D.F. Anderson, J. Park, Factorization in Subrings of K[X] or K[X], in [1], 227-241.Google Scholar
- [5]N. Bourbaki, Commutative Algebra, Hermann 1972.Google Scholar
- [6]N. Gonzales, Elasticity of A + XB[X] domains, J. Pure Appl. Algebra 138 (1999) 119–137.MathSciNetCrossRefGoogle Scholar
- [7]N. Gonzales, Elasticity and ramification, Commun. Alg. 27(4), (1999), 1729–1736.CrossRefGoogle Scholar
- [8]F. Halter-Koch, Elasticity of factorizations in atomic monoids and integral domains, J. Theor. Nombres Bordx 7 (1995), 367–385.MathSciNetMATHCrossRefGoogle Scholar
- [9]F. Kainrath, Elastizität endlich erzeugter Ringe, Thesis, Karl-Franzens-Universität Graz, Austria 1996.Google Scholar
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