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In this note, we investigate the notion of S-flat preenvelopes of modules. In particular, we give an example that a ring R being coherent does not imply that every R-module have an S-flat preenvelope, giving a negative answer to the question proposed by Bennis and Bouziri BB24. Besides, we also show that RS is a coherent ring also does not imply that R is an S-coherent ring in general.
Xiaolei Zhang (2024) studied this question.
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