منابع مشابه
Graded Integral Domains and Nagata Rings , Ii
Let D be an integral domain with quotient field K, X be an indeterminate over D, K[X] be the polynomial ring over K, and R = {f ∈ K[X] | f(0) ∈ D}; so R is a subring of K[X] containing D[X]. For f = a0 + a1X + · · ·+ anX ∈ R, let C(f) be the ideal of R generated by a0, a1X, . . . , anX n and N(H) = {g ∈ R | C(g)v = R}. In this paper, we study two rings RN(H) and Kr(R, v) = { fg | f, g ∈ R, g 6=...
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It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...
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Every Jacobi cusp form of weight k and index m over SL2(Z) Z 2 is in correspondence with 2m Dirichlet series constructed with its Fourier coefficients. The standard way to get from one to the other is by a variation of the Mellin transform. In this paper, we introduce a set of integral kernels which yield the 2m Dirichlet series via the Petersson inner product. We show that those kernels are Ja...
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Let G be a finite group and R a strongly G-graded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory answer given by Aljadeff and Robinson [3]. Another partial answer for skew group rings was given by Al...
متن کاملGraded Rings and Modules
1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2020
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2020.03.006