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In this paper we consider the class of modules of projective dimension at most one over a commutative ring and we investigate when is a covering class. More precisely, we investigate Enochs' Conjecture, that is the question of whether is covering necessarily implies that is closed under direct limits. We answer the question affirmatively in the case of a commutative semihereditary ring . This gives an example of a cotorsion pair which is not necessarily of finite type such that satisfies Enochs' Conjecture. Moreover, we describe the class over (not necessarily commutative) rings which admit a classical ring of quotients.
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Silvana Bazzoni, Giovanna Le Gros, -covers over commutative rings. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 27–43DOI 10.4171/RSMUP/54