Abstract

This paper is a natural continuation of our previous joint paper [Albu, Kara, Tercan, Fully invariant-extending modular lattices, and applications (I), J. Algebra 517 (2019), 207–222], where we introduced and investigated the notion of a fully invariant-extending lattice, the latticial counterpart of a fully invariant-extending module. In this paper we introduce and investigate the latticial counter-part of the concept of a strongly FI-extending module defined by Birkenmeier, Park, Rizvi (2002) as a module M having the property that every fully invariant submodule of M is essential in a fully invariant direct summand of M. Our main tool in doing so, is again the very useful concept of a linear morphism of lattices introduced in the literature by Albu and Iosif (2013).

摘要

本文是我们之前的联合论文 [Albu, Kara, Tercan, Fully invariant-extending modules lattices, and applications (I), J. Algebra 517 (2019), 207-222] 的自然延续，我们在其中介绍并研究了完全不变扩展格的概念，完全不变扩展模块的格对应物。在本文中，我们介绍并研究了由 Birkenmeier, Park, Rizvi (2002) 定义的强 FI 扩展模块概念的格对应部分，作为一个模块M，具有 M 的每个完全不变子模块在一个M的完全不变的直接和. 我们这样做的主要工具是Albu 和 Iosif (2013) 在文献中引入的非常有用的晶格线性态射概念。