Enveloping Classes over Commutative Rings
Bazzoni, Silvana ; Gros, Giovanna Le
arXiv, Tome 2019 (2019) no. 0, / Harvested from
Given a flat injective ring epimorphism u from commutative rings R and U, we consider the Gabriel topology G associated to u and the class D of G-divisible R-modules. We prove that D is an enveloping class if and only if it is the tilting class corresponding to a 1-tilting R-module and for every ideal J in G the quotient rings R/J are perfect rings. Equivalently, the discrete quotient rings of the topological ring End(U/R) are perfect rings. Moreover, we show that every enveloping 1-tilting class over a commutative ring arises from a flat injective ring epimorphism.
Publié le : 2019-01-23
Classification:  Mathematics - Commutative Algebra 
@article{1901.07921,
     author = {Bazzoni, Silvana and Gros, Giovanna Le},
     title = {Enveloping Classes over Commutative Rings},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.07921}
}

Bazzoni, Silvana; Gros, Giovanna Le. Enveloping Classes over Commutative Rings. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.07921/