2021/06/29 by Amzil, Houda, Bennis, Driss, Rozas, J. R. Garcia +1
#16D40 #16D50 #16D80 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2106.15592
Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. Rather than saying a module has a certain property or not, each module is assigned a relative domain which, somehow, measures to which extent it has this particular property. In this work, we introduce a new and fresh perspective on flatness of modules. However, we will first investigate a more general context by introducing domains relative to a precovering class \x. We call these domains \x-precover completing domains. In particular, when \x is the class of flat modules, we call them flat-precover completing domains. This approach allows us to provide a common frame for a number of classical notions. Moreover, some known results are generalized and some classical rings are characterized in terms of these domains.