富足半群上的F-好同余

引入了富足半群上F-好同余的概念,给出了富足半群上F-好同余的性质和特征.在此基础上,得到了富足半群上F-好同余的并为F-好同余的相关条件.最后,进一步对拟适当半群上的F-好同余作了讨论并得到了一些性质.     

F-调和映射的稳定性

本文研究了子流形的F-调和映射的稳定性.利用计算二阶变分公式的方法,得到了以欧氏空间的某些子流形为起始流形或者目标流形的稳定的F-调和映射必定是常值映射,推广了文献[3]中的结论.     

线性模型中F-检验的稳健性

本文讨论了一般线性模型中关于均值参数β的线性假设基于广义最小二乘估计的F-检验统计量的稳健性问题.主要研究了当误差的协方差矩阵含有参数时,设计阵可以列降秩情况下的F-检验统计量的稳健性,得到了F(V(θ))为该假设下F-检验统计量的误差协方差矩阵的最大类.并讨论了分块线性模型中,关于分块参数的线性假设的F-检验统计量的稳健性.     

外P集合与F-扩充数据-过滤

P-集合具有动态特性,它由内P-集合与外P-集合组成.植物品种扩充过滤过程具有外-动态特性,应用外P-集合的外-动态特性及其结构,提出了F-扩充数据概念,讨论F-扩充数据的生成与过滤,获得F-扩充数据-过滤定理及F-扩充数据的生成-过滤算法,并给出F-扩充数据-过滤的应用.研究结果为动态信息系统的数据扩充提供了一种新方法.     

复值度量空间中F-压缩映射的叠合点

将F-压缩的概念从度量空间推广到复值度量空间中,并引进F-拟压缩的概念.说明了每个F-压缩是F-拟压缩,但反之不真.运用序列逼近的方法,对两个满足某种F-压缩条件的映射,证明了 一些叠合点结果,同时得到了一些不动点结果,这些结果推广了 Wardowski的结果.给出了几个说明性例子以突出这种推广.     

F-调和映照的不存在性定理

本文主要讨论一类F-调和映照的不存在性问题,从而得到相应的Liouville型定理．     

F-展开法的扩展及应用

对F-展开法中的辅助常微分方程进行了改进,并利用改进后的常微分方程的解求得了一些重要的非线性发展方程(组)的新的Jacobi椭圆函数解,从而得到了新的孤波解.     

关于P-凸性与F-凸性的一些注记（英文）

本文得到在赋Orlicz范数(或Luxemburg范数)下Orlicz-Bochner序列空间l_M(X_s)为P-凸的当且仅当l_M是P-凸的,且{X_s}为等度P-凸的.据此可得l_M(X_s)为F-凸的当且仅当l_M是F-凸的,且{X_s}为等度F-凸的.本文也讨论了Orlicz-Bochner函数空间L_M(μ,X)中的F-凸性.     

利用F-展开法求解ZK-BBM方程

利用F-展开法求解出了ZK-BBM方程的双周期波解,并在极限形式下得到了ZK-BBM方程的孤波解和单周期波解.从而丰富了该方程解的理论.此方法也可适用求解其它非线性发展方程.     

伪单调型向量F-互补问题可行集的最小元问题

本文引入了几类向量F-互补问题并给出了向量F-互补问题与广义向量变分不等式之间的关系.通过定义向量F-互补问题的可行集,研究了伪单调型向量F-互补问题的可行集的最小问题,推广了已有的一些结果.     

ON ALMOST PRIME SUBMODULES

In this article,we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity.We study some basic properties of...     

INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

The aim of this paper is to study the conditions by which a P-prime submodule can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.     

Comultiplication submodules of multiplication modules

Abstract

All rings are commutative with identity, and all modules are unital. The purpose of this work is to investigate comultiplication submodules of multiplication modules. Various properties of this class of submodules are considered. Sufficient conditions for the sum and intersection of a finite collection of comultiplication submodules to be a comultiplication submodule are also given.     

Prime and primary submodules of certain modules

In this paper we characterize all prime and primary submodules of the free R-module R ⁿ for a principal ideal domain R and find the minimal primary decomposition of any submodule of R ⁿ . In the case n = 2, we also determine the height of prime submodules.     

Honest submodules

Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.     

On Invertible and Dense Submodules

Abstract

In this paper, the authors give a partial characterization of invertible, dense and projective submodules. In the final section, they give the equivalent conditions to be invertible, dense and projective submodules for a given an R-module M. They also provide conditions under which a given ring R is a Dedekind domain if and only if every non zero submodule of an R-module is locally free.     

$QTAG$-Modules whose $h$-Pure-$S$-High Submodules Have Closure

A right module $M$ over an associative ring $R$ with unity is a $QTAG$-module if every finitely generated submodule of any homomorphic image of $M$ is a direct sum of uniserial modules. This article considers the closure of $h$-pure-$S$-high submodules of $QTAG$-modules. Here, we determine all submodules $S$ of a $QTAG$-module $M$ such that each closure of $h$-pure-$S$-high submodule of $M$ is $h$-pure-$\overline{S}$-high in $\overline{M}$. A few results of this theme give a comparison of some elementary properties of $h$-pure-$S$-high and $S$-high submodules.     

CLOSED SUBMODULES OF NORMALIZING BIMODULES OVER SEMIPRIME RINGS

In this paper we study closed sub-bimodules of normalizing bimodules over semiprime rings. We extend the main results which are known for centred bimodules and several other results which are new even for centred bimodules are also obtained. In particular, we prove that the theorem on one-to-one correspondence between closed submodules obtained in former papers for centred bimodules is also true for normalizing bimodules. Finally, we give some applications of the main results.

     

A Construction of Relatively Pure Submodules

In this paper we reconsider a classical theorem by Bican and El Bashir, which guarantees the existence of non-trivial relatively pure submodules in a module category over a ring with unit. Our aim is to generalize the theorem to module categories over rings with several objects. As an application, we then consider the special case of α-pure objects in such module categories.     

Prime Submodules and Flat Modules

In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given.