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Keywords:
$u$-$S$-Noetherian ring; $u$-$S$-coherent ring; $u$-$S$-precover; $u$-$S$-absolutely pure module; $u$-$S$-preenvelope
$u$-$S$-Noetherian ring; $u$-$S$-coherent ring; $u$-$S$-precover; $u$-$S$-absolutely pure module; $u$-$S$-preenvelope
Summary:
We give some new characterizations of $u$-$S$-Noetherian rings and $u$-$S$-coherent rings in terms of uniform $S$-versions of injective precovers, flat preenvelopes and absolutely pure modules. Moreover, we give a negative answer to a question proposed by Bouziri.
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