2013/02/01 by Wenxi Li, WENXI LI, Jianlong Chen +3
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Annihilator #Associated prime #Chemistry #Combinatorics #Commutative Algebra and Its Applications #Computer science #Discrete mathematics #Endomorphism #Endomorphism ring #Finitely-generated abelian group #Free module #Ideal (ethics) #Integer (computer science) #Mathematics #Prime (order theory) #Pure mathematics #Ring (chemistry) #Rings, Modules, and Algebras #Zero (linguistics)
paper · doi:10.1142/s0219498813500291
openalex publication_date 2013/02/01 · crossref created 2013/02/01 · crossref issued 2013/05/16 · crossref published 2013/05/16 · crossref published-online 2013/05/16 · crossref published-print 2013/11/01 · crossref deposited 2019/08/07 · openalex created_date 2025/10/10 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/04
Let R be a ring, M R be a right R-module, n be a positive integer and S = End (M R ) be the endomorphism ring of M R . M R is called a strongly C2 module if [Formula: see text] is C2 for every positive integer m. M R is called an n-C2 module if the annihilator r M (K) ≠ 0 for any n-generated proper left ideal K of S. We prove that M R is strongly C2 if and only if M is n-C2 for every positive integer n, if and only if the annihilator r M (K) is not zero for every finitely generated proper left ideal K of S, and then we get some characterizations of right n-C2 rings and strongly right C2 rings. Also we obtain some dual statements of n-D2 module and strongly D2 module.