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91.
Raymond Mortini 《Monatshefte für Mathematik》2009,158(1):81-95
We characterize those sequences (x
n
) in the spectrum of H
∞ whose Nevanlinna–Pick interpolation problems admit thin Blaschke products as solutions. We also study under which conditions
there is a Blaschke product B with prescribed zero-set distribution and solving problems of the form B(x) = f
n
(x) for every x ∈ P(x
n
), where P(x
n
) is the Gleason part associated with the point x
n
and where (f
n
) is an arbitrary sequence of functions in the unit ball of H
∞. As a corollary we get a new characterization of Carleson–Newman Blaschke products in terms of bounded universal functions,
a result first proved by Gallardo and Gorkin.
相似文献
92.
Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case. 相似文献
93.
Chahrazade Bakkari 《代数通讯》2013,41(8):2727-2732
This article deals mainly with rings (with zerodivisors) in which regular Gaussian polynomials have locally principal contents. Precisely, we show that if (T,M) is a local ring which is not a field, D is a subring of T/M such that qf(D) = T/M, h: T → T/M is the canonical surjection and R = h ?1(D), then if T satisfies the property “every regular Gaussian polynomial has locally principal content,” then also R verifies the same property. We also show that if D is a Prüfer domain and T satisfies the property “every Gaussian polynomial has locally principal content”, then R satisfies the same property. The article includes a brief discussion of the scopes and limits of our result. 相似文献
94.
Jan Uliczka 《代数通讯》2013,41(10):3401-3409
95.
We shall introduce the notion of uniformly classical primary submodule that generalizes the concept of uniformly primary ideal as given by J. A. Cox and A. J. Hetzel. We also advance the companion concepts of fully uniformly classical primary module and uniformly primary compatible module. Along these lines, we present a characterization of Noetherian rings R for which every R-module is fully uniformly classical primary and we present a characterization of rings R for which every finitely generated R-module is uniformly primary compatible. Results illustrating connections among the notions of uniformly classical primary submodule, uniformly primary ideal, and uniformly primary submodule as given by R. Ebrahimi-Atani and S. Ebrahimi-Atani are also provided. 相似文献
96.
Let I be a squarefree monomial ideal of a polynomial ring S. In this article, we prove that the arithmetical rank of I is equal to the projective dimension of S/I when one of the following conditions is satisfied: (1) μ(I) ≤5; (2) arithdeg I ≤ 4. 相似文献
97.
A. M. Rahimi 《代数通讯》2013,41(5):1989-2004
Let R be a commutative ring with identity 1 ≠ 0. A nonzero element a in R is said to be a Smarandache zero-divisor if there exist three different nonzero elements x, y, and b (≠ a) in R such that ax = ab = by = 0, but xy ≠ 0. We will generalize this notion to the Smarandache vertex of an arbitrary simple graph and characterize the Smarandache zero-divisors of commutative rings (resp. with respect to an ideal) via their associated zero-divisor graphs. We illustrate them with examples and prove some interesting results about them. 相似文献
98.
99.
Moshe Jarden 《代数通讯》2013,41(4):1467-1494
In this paper we establish several equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of prime power ideals to be a general ZPI-ring. Using these results, we establish some equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of primary ideals to be a general ZPI-ring. 相似文献
100.
Jamilson R. Campos 《Linear and Multilinear Algebra》2013,61(3):322-346
Considering the successful theory of multiple summing multilinear operators as a prototype, we introduce the classes of multiple Cohen strongly p-summing multilinear operators and polynomials. The adequacy of these classes under the viewpoint of the theory of multilinear and polynomial ideals and holomorphy types is discussed in detail. 相似文献