Finitely generated ideals in the disk algebra
نویسندگان
چکیده
منابع مشابه
Divisibility Structure and Finitely Generated Ideals in the Disc Algebra
The main purpose of this paper is the following algebraic generalization of the corona theorem for the disc algebra A (D): I f d is a greatest common divisor of the functions f l . . . . . fn cA (D), then there exist functions gl,.",gnEA (D) with d-~flgl q-... q-fngn. This generalization is false for many algebras of holomorphic functions, e. g. in case of the Banach algebra H ~ Under the assum...
متن کاملfinitely generated closed ideals in H ∞ ( D )
© Annales de l’institut Fourier, 1985, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...
متن کاملIdeals of Denominators in the Disk-algebra
We show that there do not exist finitely generated, non-principal ideals of denominators in the disk-algebra A(D). Our proof involves a new factorization theorem for A(D) that is based on Treil’s determination of the Bass stable rank for H∞.
متن کاملPrincipal Ideals of Finitely Generated Commutative Monoids
We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.
متن کاملOn Reductions of Finitely Generated Ideals in Integral Domains
√(f1,...,fd+1)R[X] [3,p.124]. The question is whether an ideal (f1,...,fd+1) R[X] can be chosen as a reduction of I. We only know the following case of affine domains, which was developed by G. Lyubeznik [4]: Let R be an n-dimensional affine domain over an infinite field k and let I be an ideal of R. Then I has a reduction generated by n+1 elements. He also posed the following conjecture: Let A...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1994
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700013617