query: Zero divisors in polynomial in a commutative ring
positive_passages.docid: 17926
positive_passages.text: Zero divisor in $R[x]$
negative_passages.docid: 17304
negative_passages.text: Tensor product of two finitely-generated modules over a local ring is zero
negative_passages.docid: 69012
negative_passages.text: How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
negative_passages.docid: 134342
negative_passages.text: Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.
negative_passages.docid: 14343
negative_passages.text: Every nonzero element in a finite ring is either a unit or a zero divisor
negative_passages.docid: 157266
negative_passages.text: Can a nonzero polynomial evaluate to the zero function in a suitable infinite ring of char 0?
negative_passages.docid: 128213
negative_passages.text: What's the projective limit of these polynomial rings ?
negative_passages.docid: 124460
negative_passages.text: Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
negative_passages.docid: 95146
negative_passages.text: Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
negative_passages.docid: 19838
negative_passages.text: Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
negative_passages.docid: 49121
negative_passages.text: Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
negative_passages.docid: 125604
negative_passages.text: Proof that $\mathbb{Z}$ has no zero divisors
negative_passages.docid: 100340
negative_passages.text: Invariant dimension property on a ring without zero divisors
negative_passages.docid: 118532
negative_passages.text: Nilradical of polynomial ring
negative_passages.docid: 60391
negative_passages.text: Ideal Generated by Three Elements in Polynomial Ring
negative_passages.docid: 77453
negative_passages.text: A zero-dimensional ring is Noetherian?
negative_passages.docid: 115541
negative_passages.text: Subrings of polynomial rings over the complex plane