论文标题
模块上的自然部分顺序
The Natural partial order on modules
论文作者
论文摘要
米奇命令已被称为半群和环的自然部分秩序。本文的目的是通过通过内态环研究基本特性来进一步研究模块上的密施秩序。因此，这项研究也有助于与环的命令有关的结果。作为Mitsch顺序的模块理论类似物，我们表明该顺序是任意模块上的部分顺序。除其他外，研究了Mitsch顺序的晶格属性以及Mitsch秩序与其他知名订单之间的关系，例如，研究模块上的减去顺序，琼斯订单，直接总和和空间预订。特别是，我们证明了负顺序是Mitsch订单，我们提供了一个示例，以表明匡威一般不存在。
The Mitsch order is already known as a natural partial order for semigroups and rings. The purpose of this paper is to further study of the Mitsch order on modules by investigating basic properties via endomorphism rings. And so this study also contribute to the results related to the orders on rings. As a module theoretic analog of the Mitsch order, we show that this order is a partial order on arbitrary modules. Among others, lattice properties of the Mitsch order and the relations between the Mitsch order and the other well-known orders, such as, the minus order, the Jones order, the direct sum order and the space pre-order on modules are studied. In particular, we prove that the minus order is the Mitsch order and we supply an example to show that the converse does not hold in general.
