Intersection of direct summands in modules
Indian Journal of Pure and Applied Mathematics, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s13226-026-01000-x
- Dergi Adı: Indian Journal of Pure and Applied Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: idempotent lift, SIP modules, SIP-lifting modules, SSP modules
- Akdeniz Üniversitesi Adresli: Evet
Özet
We introduce and develop the class of SIP-lifting modules, refining both the Summand Intersection Property (SIP) and the lifting property. On the module side, we provide equivalent characterizations via idempotents, graph of homomorphism criteria, and radical formulations for finitely generated modules, and we give example to show the difference SIP-lifting from SIP. We also determine some class containing the new class. On the ring side, we translate SIP-lifting into idempotent conditions controlling intersections inside the Jacobson radical and obtain new characterizations of classical classes: a ring is semiperfect iff every finitely generated module is SIP-lifting, and perfect iff every module is SIP-lifting. These results connect idempotent lifting and radical with decomposition and cover theory, yielding a unified framework that extends and sharpens known SIP/lifting (D1) phenomena.