易熔模块

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2023-07-29 DOI:10.15672/hujms.1206395

Işıl BAYDAR, Burcu ÜNGÖR, Sait HALİCİOGLU, Abdullah HARMANCI

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引用次数: 0

摘要

本文通过引入易熔模块，将易熔性的概念扩展到模块理论的设定中。设$R$是一个带单位元的环，$M$是一个右$R$-模，$0\neq M \在M$中。如果$m$可以表示为$m$中的一个扭转单元和一个无扭转单元的和，则$m$称为{\it fusible}。如果模块$M$的每个非零元素都是可熔的，则称模块$M$是可熔的。研究了易熔模块的一些性质。证明了可熔模类介于无扭模类和非奇异模类之间。

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Fusible Modules

In this paper we extend the concept of fusibility to the module theoretic setting by introducing fusible modules. Let $R$ be a ring with identity, $M$ a right $R$-module and $0\neq m\in M$. Then $m$ is called {\it fusible} if it can be expressed as the sum of a torsion element and a torsion-free element in $M$. The module $M$ is said to be {\it fusible} if every non-zero element of $M$ is fusible. We investigate some properties of fusible modules. It is proved that the class fusible modules is situated between the classes of torsion-free modules and nonsingular modules.

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来源期刊

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.