In the definition of localization of a ring $R$, why do we require the existence of $t$ in the multiplicative subset to define the equiv relation?
73689
A question about the equivalence relation on the localization of a ring.
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
5084
When is the completion of a ring a local ring ?
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
120235
Clarification of the notation $f: \mathbb{R} \setminus\{3\} \to\mathbb{R}\setminus\{2\}$
28272
Does such localization of integral extension preserve inclusion?
130159
Meaning of ring notation $\Bbb Z_{(p)}$ in commutative algebra [localization]
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
109039
Does this "extension property" for polynomial rings satisfy a universal property?
24259
Quotient ring of $T/I$
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
104747
Does localisation commute with Hom for finitely-generated modules?