Super-additive Sequences and Algebras of Polynomials
نویسنده
چکیده
If K is a field with discrete valuation ν and D = {a ∈ K : ν(a) ≥ 0}, then an algebra D[x] ⊆ A ⊆ K[x] has associated to it a sequence of fractional ideals {In : n = 0, 1, 2, . . . } with In consisting of 0 and the leading coefficients of elements of A of degree no more than n and a sequence of integers {a(n) : n = 0, 1, 2, . . . } with a(n) = −ν(In). Combinatorial properties of this integer sequence reflect algebraic properties of A, and these are used to identify the degrees of generators of A and to characterize finitely generated algebras A by a periodicity property of this sequence.
منابع مشابه
Generalized additive functional inequalities in Banach algebras
Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)| le |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...
متن کاملContinuity of super- and sub-additive transformations of continuous functions
We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.
متن کاملSUPER- AND SUB-ADDITIVE ENVELOPES OF AGGREGATION FUNCTIONS: INTERPLAY BETWEEN LOCAL AND GLOBAL PROPERTIES, AND APPROXIMATION
Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {it Fuzzy Sets and Systems} {bf 291} (2016), 40--53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with ...
متن کاملOn the operad of associative algebras with derivation
We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to the operad of “moulds”. It provides an efficient environment for doing integro-differential calculus. Interesting variations are obtained by using formal grou...
متن کاملA Quantum Analog of the Poincare–birkhoff–witt Theorem
We reduce the basis construction problem for Hopf algebras generated by skew-primitive semi-invariants to a study of special elements, called “super-letters,” which are defined by Shirshov standard words. In this way we show that above Hopf algebras always have sets of PBW-generators (“hard” super-letters). It is shown also that these Hopf algebras having not more than finitely many “hard” supe...
متن کامل