Topic
Free module
About: Free module is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 9812 citations.
Papers published on a yearly basis
1 / 2
Papers
400 citations
Journal Article•
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TL;DR: In this article, the authors define small submodules of a module M over R over a ring with identity, M is a module over R, G is an abelian group of finite rank, E is the ring of endomorphisms of G and S is the center of E.
Abstract: The concept of a continuous module is a generalization of that of an injective module, and conditions (), (C) and () are given for this concept in [4]. In this paper, we study modules with properties that are dual to continuity. These will be called discrete and we discuss discrete abelian groups. Throughout R is a ring with identity, M is a module over R, G is an abelian group of finite rank, E is the ring of endomorphisms of G and S is the center of E. Dual to the notion of essential submodules, we define small submodules of a module M over R.(omitted)
295 citations
TL;DR: In this article, Kilmer et al. define a free module and show that every linear transformation on that module can be represented by tensor multiplication, and present a generalization of ideas of eigenvalue and eigenvector to the space of n × n-times-n tensors.
253 citations
221 citations
TL;DR: In this paper, it was shown that the homotopy category K(R-Proj) is always ''aleph_1\)-compactly generated, and that depending on the ring R, it may or may not be compactly generated.
Abstract: Let R be a ring. We prove that the homotopy category K(R-Proj) is always \(\aleph_1\)-compactly generated, and, depending on the ring R, it may or may not be compactly generated. We use this to give a description of K(R-Proj) as a quotient of K(R-Flat). The remarkable fact is that this new description of K(R-Proj) generalizes to non-affine schemes; this will appear in Murfet’s thesis.
213 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 14 |
| 2020 | 13 |
| 2019 | 13 |
| 2018 | 17 |
| 2017 | 30 |