A question regarding the definition of localization of ring
4507
Localization of a ring which is not a domain
124646
Understanding the ideal $IJ$ in $R$
5084
When is the completion of a ring a local ring ?
18036
Localization by a non-nilpotent as a polynomial quotient
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
98818
Quotient ring of a localization of a ring
72507
Does $ab=1$ imply $ba=1$ in a ring?
10908
Associated elements in a ring
56020
Localization and flatness
157605
$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$
52966
Rings, ideals and units-proof
34990
Ring homomorphism defined on a field
145933
Localization commutes with Hom for finitely-generated modules
42871
Quotient of a local regular ring
104747
Does localisation commute with Hom for finitely-generated modules?
48818
Homomorphism of local rings
45684
Is quotient of a ring by a power of a maximal ideal local?