On flat epimorphisms of rings and pointwise localizations | Zendy

Abolfazl Tarizadeh | Zendy

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On 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 , pure mathematics , ideal (ethics) , minimal ideal , associated prime , commutative ring , ring (chemistry) , von neumann regular ring , 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.

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