Show that $A[X]/(aX+b)$ is an integral domain
50665
If $a,b$ is an $R$-sequence, then $ax-b$ is prime (Eisenbud, Exercise 10.4)
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
141659
Every field is an integral domain
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
44737
$ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
52902
How to prove $\int_{\mathbb R^d}{(1+|x|^{2})^{-m}dx}$ is integrable?
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
70193
Show that the relation defined on an integral domain by "$x\sim y$" ("$x$ is associated with $y$") is a relation of equivalence.
33944
Describe $\mathbb{R}[x]/(x^{2}+ax+b)$ where $a,b \in \mathbb{R}$
58424
If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
138025
How to show the solution of $\dot{x} = Ax $ is an invariant subspace?
31049
If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible