The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding based on the solutions certain associated polynomial equations. proposed also makes it possible to identify conditions existence sought schemes.

Let D be an integral domain and E = {e1, . . . , ek} a finite nonempty subset of D. Then Int(E,D) has the strong two-generator property if and only if D is a Bezout domain. If D is a Dedekind domain which is not a principal ideal domain, then we characterize which elements of Int(E, D) are strong two-generators. Let D be an integral domain with quotient field K and E ⊆ D a subset of D. We let I...

We study projective completions of affine algebraic varieties which are given by filtrations, or equivalently, ‘degree like functions’ on their rings of regular functions. For a quasifinite polynomial map P (i.e. with all fibers finite) of affine varieties, we prove that there are completions of the source that do not add points at infinity for P (i.e. in the intersection of completions of the ...

Suppose R is a Bezout domain. In this paper, some necessary and sufficient conditions for the existence of the group inverse for square matrix over R are given, the conditions for the existence of the group inverse of products of matrices are studied, and the equivalent conditions for reverse order law of group inverse of product of matrices are obtained. Also the existence and the representati...

the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.