𝒫 1 -covers over commutative rings
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 27-43.
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In this paper we consider the class 𝒫 1 (R) of modules of projective dimension at most one over a commutative ring R and we investigate when 𝒫 1 (R) is a covering class. More precisely, we investigate Enochs' Conjecture, that is the question of whether 𝒫 1 (R) is covering necessarily implies that 𝒫 1 (R) is closed under direct limits. We answer the question affirmatively in the case of a commutative semihereditary ring R. This gives an example of a cotorsion pair (𝒫 1 (R),𝒫 1 (R) ⊥ ) which is not necessarily of finite type such that 𝒫 1 (R) satisfies Enochs' Conjecture. Moreover, we describe the class lim →𝒫 1 (R) over (not necessarily commutative) rings which admit a classical ring of quotients.

Publié le :
DOI : 10.4171/rsmup/54
Classification : 13, 18 
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     author = {Bazzoni, Silvana and Le Gros, Giovanna},
     title = {$\mathcal P_1$-covers over commutative rings},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {27--43},
     volume = {144},
     year = {2020},
     doi = {10.4171/rsmup/54},
     mrnumber = {4186444},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/54/}
}
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Bazzoni, Silvana; Le Gros, Giovanna. $\mathcal P_1$-covers over commutative rings. Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 27-43. doi : 10.4171/rsmup/54. http://www.numdam.org/articles/10.4171/rsmup/54/

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