Makale detayı · 2000
On lifting modules
- Yıl
- 2000
- Tür
- article
Veri kaynağı ayrımı
- YÖKSİS YÖKSİS makale kaydı
- YÖKSİS dergi adı Communications in Algebra
- Katalog eşleşmesi (ISSN) Communications in Algebra
- OpenAlex OpenAlex zenginleştirmesi (özet, atıf, konular)
Özet
OpenAlex · İngilizce
Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for all 1 ≤ i ≤ n.Let be a finite direct sum of R-modules Mi . We prove that M is (quasi-) discrete if and only if are relatively projective (quasi-) discrete modules. We also prove that, for an amply supplemented R-module M=M 1⊕M 2 such that M 1 and M 2 have the finite exchange propertyM is lifting if and only if M 1 and M 2 are lifting and relatively small projective R-modules and every co-closed submodule N of M with M= N+M 1 = N+M 2 is a direct summand of M.Finally, we prove that, for a ring Rsuch that every direct sum of a lifting R-module and a simple R-module is lifting, every simple R-module is small M-projective for any lifting R-module M.
Konular
Atıflar
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87 atıf
OpenAlex cited_by_count (önbellek / veritabanı)
Yerel katalogda bu makaleye atıf yapan 17 yayın (OpenAlex referans eşleşmesi; tam dünya listesi değildir).
- On Å Supplemented Modules 1999
- ON HOLLOW-LIFTING MODULES 2007
- Generalizations of Lifting Modules 2001
- On H-Supplemented Modules 2011
- CHARACTERIZATIONS OF LIFTING MODULES IN TERMS OF COJECTIVE MODULES AND THE CLASS OF ℬ(M,X) 2005
- ON GENERALIZED EPI-PROJECTIVE MODULES 2010
- Correspondences of Coclosed Submodules 2013
- Rad-Discrete Modules 2021
- Rad-Discrete Modules 2021
- Goldie-Rad-Supplemented Modules 2014