模格中的Goldie绝对直接和

IF 0.3 Q4 MATHEMATICS Mathematica Bohemica Pub Date : 2022-07-11 DOI:10.21136/mb.2022.0110-21

R. Shroff

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引用次数: 0

摘要

.定义了格中的绝对直和，并研究了它在模格中的一些性质。证明了在一类模格中，两个元素的直和具有绝对直和当且仅当这些元素是相对内射的。作为绝对直接被加数（简称ADS）的推广，引入并研究了格中Goldie绝对直接被加数的概念。结果表明，Goldie-ADS性质是由直接和数继承的。给出了模格单元具有Goldie ADS的一个充要条件。

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On Goldie absolute direct summands in modular lattices

. Absolute direct summand in lattices is deﬁned and some of its properties in modular lattices are studied. It is shown that in a certain class of modular lattices, the direct sum of two elements has absolute direct summand if and only if the elements are relatively injective. As a generalization of absolute direct summand (ADS for short), the concept of Goldie absolute direct summand in lattices is introduced and studied. It is shown that Goldie ADS property is inherited by direct summands. A necessary and suﬃcient condition is given for an element of modular lattice to have Goldie ADS.

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来源期刊

Mathematica Bohemica MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

52 weeks