Given a module M over an arbitrary ring, we characterize the existence of Add M -covers and Add M -envelopes in terms of finiteness conditions of M over its endomorphism ring. We also give some applications related to the existence of well-behaved direct sum decompositions for direct products of copies of M. These results can be viewed as natural extensions of classical theorems of Bass and Chase on coherent and perfect rings.
On some precovers and preenvelopes
ANGELERI, LIDIA
2000-01-01
Abstract
Given a module M over an arbitrary ring, we characterize the existence of Add M -covers and Add M -envelopes in terms of finiteness conditions of M over its endomorphism ring. We also give some applications related to the existence of well-behaved direct sum decompositions for direct products of copies of M. These results can be viewed as natural extensions of classical theorems of Bass and Chase on coherent and perfect rings.
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