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[1] Yao Lingling, Chen Jianlong,. A generalization of co-*nn-modules [J]. Journal of Southeast University (English Edition), 2010, 26 (3): 505-508. [doi:10.3969/j.issn.1003-7985.2010.03.028]
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A generalization of co-*nn-modules()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
26
Issue:
2010 3
Page:
505-508
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2010-09-30

Info

Title:
A generalization of co-*nn-modules
Author(s):
Yao Lingling;  Chen Jianlong
Department of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
co-*∞-module;  ∞-quasi-injective;  co-selfsmall;  co-*nn-module
PACS:
O154.2
DOI:
10.3969/j.issn.1003-7985.2010.03.028
Abstract:
A module is called a co-*∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-*∞-module, the functor Hom RURU(-, U)is exact in Copres∞(U). A module U is a co-*∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞(U)and I is a set, N∈Copres∞(U)is equivalent to Ext1RR(N, U)→Ext1RR(UI, U)is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞(U), N∈Copres∞(U)is equivalent to the induced sequence 0→Δ(N)→Δ(M)→Δ(L)→0 which is exact if and only if U induces a duality ΔUS:⊥US⇔Copres∞(U):ΔRURU. Moreover, U is a co-*nn-module if and only if U is a co-*∞-module and Copres∞(U)=Copresnn(U).

References:

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Memo

Memo:
Biographies: Yao Lingling(1982—), female, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10971024), Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024).
Citation: Yao Lingling, Chen Jianlong.A generalization of co-*nn-modules[J].Journal of Southeast University(English Edition), 2010, 26(3):505-508.
Last Update: 2010-09-20