It is shown that the ideal theories of the fields of all meromorphic functions on any two noncompact Riemann surfaces are isomorphic. Further, various new representation and factorization theorems are proved. Introduction. Throughout this paper let X and Y denote noncompact (connected) Riemann surfaces. Let A(X) (or A for short), denote the ring of all analytic functions on X, and let F(X) (or ...

Here we study the maximal dimension of the annihilator ideals 0 :A m j of artinian graded rings A = P/(I, x1, x 2 2, . . . , x 2 v) with a given Hilbert function, where P is the polynomial ring in the variables x1, x2, . . . , xv over a field K with each deg xi = 1, I is a graded ideal of P , and m is the graded maximal ideal of A. As an application to combinatorics, we introduce the notion of ...

Let A be a unital complex semisimple Banach algebra, and MA denote its maximal ideal space. For matrix M∈An×n, Mˆ denotes the obtained by taking entry-wise Gelfand transforms. M∈Cn×n, σ(M)⊂C set of eigenvalues M. It is shown that if A∈An×n B∈Am×m are such for all φ∈MA, σ(Aˆ(φ))∩σ(Bˆ(φ))=∅, then C∈An×m, Sylvester equation AX−XB=C has unique solution X∈An×m. As an application, Roth's removal rule...

We continue the study of the Newton polytope Pm,n of the product of all maximal minors of an m x n-matrix of indeterminates. The vertices of Pm,n are encoded by coherent matching fields A = (A z) , where z runs over all m-element subsets of columns, and each Az is a bijection z —> [m]. We show that coherent matching fields satisfy some axioms analogous to the basis exchange axiom in the matroid...