2016/08/20 by Tarizadeh, Abolfazl
#13B10 #13C11 #14A05 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1608.05835
In this paper all rings are commutative. We prove some new results on flat epimorphisms of rings and pointwise localizations. Especially among them, it is proved that a ring R is an absolutely flat (von-Neumann regular) ring if and only if it is isomorphic to the pointwise localization R(-1)R, or equivalently, each R-algebra is R-flat. For a given minimal prime ideal \mathfrakp of a ring R, the surjectivity of the canonical map R→ R_\mathfrakp is characterized. Finally, we give a new proof to the fact that in a flat epimorphism of rings, the contraction-extension of an ideal equals the same ideal.