9
votes

Accepted

### What is the intersection of all ideals whose radicals are prime?

Is the intersection of all fuzzy primes $\{0\}$?
Not always. Let me describe a commutative ring where the intersection of the fuzzy primes is nonzero.
Plan. The idea will be to construct a commutative ...

4
votes

Accepted

### A question about surjective maps between quadratic algebras

There are plentiful examples of $m$-generated quadratic algebras $A$ with $A_3 = 0$, and dimension of relation subspace $R$ being as low as $m^2/2$. One of those algebras is $$\Bbb k\langle x_1, y_1, \...

2
votes

### What is the intersection of all ideals whose radicals are prime?

This is not true, and we can produce explicit examples by applying standard modifications (quotients, fibre products) to higher rank valuation rings.
Example. Let $M$ be the submonoid of $\mathbf Z^2$ ...

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