The concept of right (left) quotient (or residual) of an ideal η by anideal ν of an L-subring μ of a ring R is introduced. The right (left) quotients areshown to be ideals of μ . It is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an L-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . Most of the results pertaining to the notion of quotients(or residual) of ...

Orthogonality of polynomials in several variableswith respect to a positiveBorelmeasure supported on an algebraic set is themain theme of this paper.As a step towards this goal quasi-orthogonality with respect to a non-zero Hermitian linear functional is studied in detail; this occupies a substantial part of the paper. Therefore necessary and sufficient conditions for quasi-orthogonality in ter...

Abstract Let K K be an imaginary quadratic field different from Q ( − 1 ) {\mathbb{Q}}\left(\sqrt{-1}) and 3 {\mathbb{Q}}\left(\sqrt{-3}) . For a nontrivial integral ideal ma...

We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous work, we defined general syntactic conditions based on the notion of computable closure for ensuring the termination of the combination of rewriting and beta-re...

We study the algebra U ζ obtained via Lusztig's 'integral' form [Lu 1, 2] of the generic quantum algebra for the Lie algebra g = sl 2 modulo the two-sided ideal generated by K l − 1. We show that U ζ is a smash product of the quantum deformation of the restricted universal enveloping algebra u ζ of g and the ordinary universal enveloping algebra U of g, and we compute the primitive (= prime) id...