Some remarks on Lucas modules
Xiaolei Zhang, Guocheng Dai, Wei Qi
TL;DR
This paper explores properties of Lucas modules, demonstrating their stability under limits, existence of envelopes and covers, and analyzing their construction and mapping properties.
Contribution
It establishes that direct and inverse limits of Lucas modules are Lucas modules and proves the existence and properties of Lucas envelopes and covers.
Findings
Limits of Lucas modules remain Lucas modules
Every module has a Lucas envelope and cover
Properties of limits and constructions of Lucas modules are characterized
Abstract
In this paper, we discuss some properties on Lucas modules. In details, we show that direct and inverse limits of Lucas modules are Lucas modules, and every -module has a Lucas envelope and a Lucas cover. Moreover, some properties of direct and inverse limits of Lucas modules and some constructions and the unique mapping properties of Lucas envelopes and Lucas covers are investigated.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Mathematical Theories and Applications · Topological and Geometric Data Analysis