Lidia Angeleri-Hügel

Let $R$ be a ring and $M_R$ be an $R$-module. We characterize the existence of ${\rm Add} M$-covers and ${\rm Add} M$-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 Mathematical Subject Classification: 16D90, 16G10, 16S50, 16D40, 16P70, 16E50.

Keywords: left/right approximations, endomorphism ring, matrix subgroup, perfect rings, coherent rings.

E-mail: angeleri@rz.mathematik.uni-muenchen.de