unique factorization domain

Inthis paper,we summarize some sufficient criteria about anirreducible polynomial of degree n over aunique factorization domain R.

修改文献[6]中定理的条件,获得了两个判别唯一分解整环R上偶次多项式不可约的充分性定理,并得到了两个新的推论。

We give a method of determining irreducible polynomials over a unique factorization domain.

给出了唯一分解整环上多项式不可约的一个判别法。

In this paper, we obtain a sufficient condition that a polynomial of degree n (n>2) is irreducible over a unique factorization domain R or its quotient field.

本文获得了一个判别唯一分解整环R及其商域Q上的n次 (n >2 )多项式不可约的充分条

From field to unique factorization domain and its application;

从域到唯一分解环及其应用

On the unique factorization domain,it gives the generalized result about the system of bivariate homogeneous nonconstant polynomials, and hence obtains the generalized result about the system of univariate nonconstant polynomials.

推广了ＫｕｎｉｏＫａｋｉｅ定理，得到了其在唯一分解环上关于一般二元齐次非常元多项式系的相应结果；并进一步给出了其在唯一分解环上关于一般一元非常元多项式系的对应形式。

This paper generalizes the classical result, the existence criterion of nonconstantcommon divisors of two polynomials in the polynomial ring R[ x], and obtains the corresponding result abeut a general polyndrial system in the polynmial ring R[x], where R isan unique factorization domain.

推广了经典结果，即唯一分解环R上多项式环R[x]中两个多项式的非常无公因子存在性判别准则，得到了唯一分解环R上多项式环R[x]中的一般多项式系与之相应的结果。

If R is an unique factorization ring,then so is R[x,x ~ -1 ].

若R是一个唯一分解环 ,则R[x ,x- 1 ]是唯一分解环 。

Criteria of Irreducible Polynomials over an Unique Factorization Domain R;

唯一分解整环R上不可约多项式的一些判别准则

Factorization in Rings of Polynomials in One Indeterminate Over a Unique Factorization Domain;

唯一分解环上的一元多项式环的因子分解

The Global Existence and Uniqueness of Solution to the Nonlinear Population PDE Model;

一类非线性人口偏微分模型整体解的存在唯一性

The existence and uniqueness of global solution for a kind of partial differentions on the human population mathematical model with immigration;

带移民因素的一类偏微分人口模型整体解的存在唯一性

Smith Matrices for an U.F.D.;

惟一因子分解整环上的Smith矩阵

Uniqueness of Positive Radial Solutions for Dirichlet Problems in an Annulus

环形区域上Dirichlet问题正径向解的唯一性

Uniqueness of Entire Functions Concerning One Shared-set

具有一个分担集合的整函数的唯一性

The Existence and Uniqueness of the Solution to Cauchy Problem of Heat Equation;

一类热传导方程Cauchy问题整体解的存在唯一性

Uniqueness Theory on Entire Functions and Their Linear Differential Polynomials;

整函数与其微分多项式的唯一性理论

The Uniqueness about Entire Functions Sharing Two CM Values;

具有2个CM分担值整函数的唯一性

Uniqueness of Entire Function Sharing a Set with Its Dirivative

整函数与其导函数分担值集的唯一性

On the Global Existence and Uniqueness of Solutions to the Non-Stationary Boundary Layer Systems;

非定常边界层问题整体解的存在性及唯一性

Global Existence and Uniqueness of Solution for a Fast Reaction-diffusion Equation;

快速反应扩散方程解的整体存在唯一性

The Existence and Uniqueness of the Solution to a Class of Differential Equations

一类微分方程的解的存在性和唯一性

Existence and Uniqueness of Solutions to a kind of Partial Functional Differential Equation

一类偏泛函微分方程解的存在唯一性

Existence and Uniqueness of Solutions to Singular Differential Equations;

非线性奇异微分方程解的存在唯一性

Decomposition of Complete Lie Color Algebra and Uniqueness;

完备李Color代数的分解唯一性

Uniqueness of A Class of Nonlinear Parabolic Inverse Problems;

抛物型偏微分方程反问题解的唯一性