Duality between injective envelopes and flat covers

Puuska, Ville (2023-04-05)
 
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Puuska, Ville
05.04.2023

JOURNAL OF PURE AND APPLIED ALGEBRA
107542
doi:10.1016/j.jpaa.2023.107542
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https://urn.fi/URN:NBN:fi:tuni-202311109562

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We establish a duality between injective envelopes and flat covers over a commutative Noetherian ring. One case of this duality states that a morphism is an injective envelope, if and only if its Matlis dual is a flat cover. We also show that if we swap injective envelopes and flat covers in this duality, neither implication is true in general.

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