for each  and i ≥ 0. The polynomial ring of integer-valued in rational  is defined by Int (    an important example binomial and is non-Noetherian ring. In this paper the algebraic structure rings has been studied their properties ideals. notion ideal generated a given set defined.  Which allows us to define new class Noetherian using ideals, which we named it binomiall...

This talk will provide a snapshot of contemporary commutative algebra. In classical commutative algebra and algebraic number theory, the Dedekind domains are the most important class of rings. Modern commutative algebra studies numerous generalizations of the Dedekind domains in attempts to generalize results of algebraic number theory. This talk will introduce a few important generalizations o...

Contents 1. Introduction 963 2. A game called í µí±ƒ-orderings 967 2.1. On í µí±Ÿ-removed í µí±ƒ-orderings 968 2.2. On í µí±ƒ-orderings of order ℎ 969 3. Rings of integer-valued polynomials 969 3.1. Polynomials with integer-valued divided differences 970 3.2. Integer-valued polynomials having a given modulus 973 4. Smooth functions on compact subsets of local fields 976 4.1. The Banach space of...

The Classical statistical inference for integer valued time-series has primarily been restricted to the integer valued autoregressive (INAR) process. Markov chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches of statistics and is particularly well suited to integer valued time-series where statistical inference is greatly assisted by data augmentation. Thus in ...

When D is an integral domain with field of fractions K, the ring Int(D) = {f(x) ∈ K[x] | f(D) ⊆ D} of integer-valued polynomials over D has been extensively studied. We will extend the integer-valued polynomial construction to certain noncommutative rings. Specifically, let i, j, and k be the standard quaternion units satisfying the relations i = j = −1 and ij = k = −ji, and define ZQ := {a+bi+...

Integer-valued polynomials on subsets of discrete valuation domains are well studied. We undertake here a systematical study of integer-valued polynomials on subsets S of valued fields and of several connected notions: the polynomial closure of S, the Bhargava’s factorial ideals of S and the v-orderings of S. A sequence of numbers is naturally associated to the subset S and a good description c...

This paper focuses on different methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predict...