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单词 FaithfullyFlat
释义

faithfully flat


Let A be a commutative ring. Then M if faithfully flat if for any A-modules P,Q, and R, we have

0PQR0

is exact if and only if the M-tensored sequence

0MAPMAQMAR0

is exact. (Note that the “if and only if” clause makes this stronger than the definition of flatness).

Equivalently, an A-module M is faithfully flat iff M is flat and the functorMathworldPlanetmath -AM is a faithful functorMathworldPlanetmath (and hence the name).

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更新时间:2025/5/4 17:06:23