Showing integrality of a certain ring
7903
Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
98818
Quotient ring of a localization of a ring
66451
In a ring, how do we prove that a * 0 = 0?
30714
A question on ring homomorphisms and maximal ideals.
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
73689
A question about the equivalence relation on the localization of a ring.
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
105913
Calculations in quotient rings
108601
Show structure of a commutative ring in a tensor product
133975
Localising a polynomial ring and non-maximal prime ideal
107900
A ring which has many distinct left inverses
157488
Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
55902
Show $R[x]/(x)\cong R$
129438
Gaussian Integers and Quotient Rings