R integral domain, Q its field of fraction, M R-module with nontrivial annihilator. Is Ext(Q,M) always 0?
109647
Ext$_R^n(Q,A)=0=$Tor$_n^R(Q,A)$ where $Q$ is the field of fractions of a domain $R$
102072
Simple $M_n(D)$-module with $D$ a division ring
23242
Commutative integral domain with d.c.c. is a field
41398
For a ring $R$, does $\operatorname{End}_R(R)\cong R^{\mathrm{op}}$?
68790
Do we have $K(\beta)=K(\beta^2)$ for field extension of odd degree?
93621
Prove that $\mathbb{Z}[\omega]$ is an integral domain
63338
Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?
142699
Is $R/N(R)$ a faithfully flat $R$-module?
147722
Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?
18887
Euclidean domain in which the quotient and remainder are always unique
105141
$\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
140474
Why is Ext$(-;k) =0$ when $k$ is a field
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
132193
Why $\Bbb Z$ = (integers) is an integral domain?
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?