-covers over commutative rings

  • Silvana Bazzoni

    Università degli Studi di Padova, Italy
  • Giovanna Le Gros

    Università degli Studi di Padova, Italy
$\mathcal P_1$-covers over commutative rings cover
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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.

Cite this article

Silvana Bazzoni, Giovanna Le Gros, -covers over commutative rings. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 27–43

DOI 10.4171/RSMUP/54