Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

Number of ways to color the edges of a tetrahedron with two colors?

An unbiased coin is tossed six times in a row. Which statement describing the last two coin tosses has the highest probability of being correct?

Why in Quotient Group we need normal subgroup?

$\mathcal{L}(V,W)$ is infinite dimensional when $V$ is finite dimensional and $W$ is infinite dimensional.

Which branch of mathematics rigorously defines infinitesimals?

If $A$ is a self-adjoint operator . Is $\|A^n\|=\|A\|^n,\;\forall n$?

How to calculate the integral $\int\frac{1}{\sqrt{(x^2+8)^3}}dx$?

An interesting integral $\cos(x)\cos(x^2)\cos(x^3)...$

Compute $\int\frac{x}{x+1}dx$

Is a function periodic $f(x) = \cos (x) +\cos(x^2)$

Finding the limit of a sequence of integrals

Show that $ \sum_{k=0}^{n} \binom{2n+1}{2k} 3^k $ is divisible by $2^n$

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