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Covers and Envelopes via Endoproperties of Modules
Author(s) -
AngeleriHügel Lidia
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s002461150201393x
Subject(s) - mathematics , endomorphism ring , bass (fish) , ring (chemistry) , endomorphism , mathematics subject classification , discrete mathematics , pure mathematics , ecology , chemistry , organic chemistry , biology
Let R be a ring and M R be an R ‐module. We characterize the existence of Add M ‐covers and Add M ‐envelopes in terms of finiteness conditions of M over its endomorphism ring. We then present some applications related to the existence of well‐behaved direct sum decompositions for direct products of copies of M . Our results can be viewed as natural extensions of classical theorems of Bass and Chase on coherent and perfect rings. 2000 Mathematics Subject Classification 16D90, 16G10, 16S50, 16D40, 16P70, 16E50.