n this article, we prove An Lp-Lq-version of Morgan’s theorem for the generalized Bessel transform.

Let R be a commutative ring throughout. Usually R will be an integral domain and even a principal ideal domain, but these assumptions will be made explicitly. Since R is commutative, there is no distinction between left, right and 2-sided ideals. In particular, for every ideal I we have a quotient ring R/I. F always denotes a field. Our goal is to prove the classification theorem for finitely-g...

Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set   of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where   $mathbb{P}(R)$ is...

The purpose of this note is to collect some theorems and proofs related to integrality in commutative algebra. The note is subdivided into three parts. Part 1 (Integrality over rings) consists of known facts (Theorems 1, 4, 5) and a generalized exercise from [1] (Corollary 3) with a few minor variations (Theorem 2 and Corollary 6). Part 2 (Integrality over ideal semifiltrations) merges integral...

1 Introduction. In this paper, two players alternate removing a positive number of counters from one of n piles of counters, and the choice of which pile he removes from can change on each move. On his initial move, the player moving first can remove from one pile of his choice at most t counters. On each subsequent move, a player can remove from one pile of his choice at most f (x) counters, w...

It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky’s theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, Bézout domain, valuation domain, Krull domain, π-domain).

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

We discuss the relationship between the classical Lagrange theorem in mathematics and the quantum statistical mechanics and thermodynamics of an ideal gas of multispecies quasiparticles with mutual fractional exclusion statistics. First, we show that the thermodynamic potential and the density of the system are analytically expressed in terms of the language of generalized cluster expansions, w...

In this note we show that the quotient field of a domain which is Henselian with respect to a non-trivial ideal is a large field, and give some applications of this fact, using a specialization theorem for ramified covers of the line over (generalized) Krull fields.

our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...