A non-zero ring $R$ is a field if and only if for any non-zero ring $S$, any ring homomorphism from $R$ to $S$ is injective.

Finding all the maximal ideals of $C([0,1])$ and also prime ideals in it which are not maximal

Is there Any Homomorphism Between Vector Spaces that is not Linear?

Is $\langle x^2+1,y\rangle$ maximal or prime in $\Bbb{R}[x,y]$ or $\Bbb{C}[x,y]$

In classical geometry why is a line considered to be parallel to itself?

Evaluate $\lim_{n\to \infty} \left( \sum_{r=0}^n \frac {2^r}{5^{2^r}+1}\right) $

The Plucker relations are sufficient

If derivative of $f$ is continuous, then $f$ is continuous.

Arithmetic sequence where every term is prime?

Intuition behind Lagrange multiplier

Unexpected use of topology in proofs

What is $x$, if $\cot ^{-1} \left(3x+\frac{2}{x}\right)+\cot ^{-1} \left(6x+\frac{2}{x}\right)+\cot ^{-1} \left(10x+\frac{2}{x}\right)+\cdots = 1$?

$S$ is closed under pairwise unions $⇒$ $S$ is closed under arbitrary unions?

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