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Large subdirect products of flat modules. (English) Zbl 0845.16003
The authors look at the problem of when every \(\aleph\)-product [cf. J. Dauns, Pac. J. Math. 126, 1-19 (1987; Zbl 0597.16020)] of copies of a given flat right \(R\)-module \(U\) is flat, where \(\aleph\) is an infinite cardinal number. They characterize these modules in terms of a sort of “relative coherence” of the ring \(R\) with respect to the module \(U\) and the cardinal \(\aleph\). In the last part of the paper they give some applications to the endomorphism ring \(S\) of \(U\), determining when \(\aleph\)-products of \(S_S\) are either flat or projective.

MSC:
16D40 Free, projective, and flat modules and ideals in associative algebras
16S60 Associative rings of functions, subdirect products, sheaves of rings
16S50 Endomorphism rings; matrix rings
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)
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References:
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