Open AccessOn flat epimorphisms of rings and pointwise localizations
Author(s) -
Abolfazl Tarizadeh
Publication year - 2022
Publication title -
mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.294
H-Index - 6
eISSN - 2601-744X
pISSN - 1222-9016
DOI - 10.24193/mathcluj.2022.1.14
Subject(s) - epimorphism , mathematics , pointwise , subring , minimal ideal , pure mathematics , ideal (ethics) , commutative ring , associated prime , ring (chemistry) , maximal ideal , discrete mathematics , combinatorics , prime (order theory) , commutative property , mathematical analysis , philosophy , chemistry , organic chemistry , epistemology
We prove some new results on flat epimorphisms of commutative 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 p of a ring R, the surjectivity of the canonical map from R to R_p 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.