query: Zero in the polynomial ring
positive_passages.docid: 157266
positive_passages.text: Can a nonzero polynomial evaluate to the zero function in a suitable infinite ring of char 0?
negative_passages.docid: 145191
negative_passages.text: Content of a polynomial
negative_passages.docid: 34183
negative_passages.text: An equivalent condition with $\{0\}$ being the only nilpotent ideal
negative_passages.docid: 5802
negative_passages.text: Proving the universal mapping property for polynomial rings
negative_passages.docid: 35222
negative_passages.text: Characterizing units in polynomial rings
negative_passages.docid: 128043
negative_passages.text: $A^n=0$ for $A$ nilpotent without the use of minimal polynomial
negative_passages.docid: 10585
negative_passages.text: Does a polynomial that's bounded below have a global minimum?
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 104233
negative_passages.text: Is the ring of the polynomials on a finite algebraic set always a product of local rings?
negative_passages.docid: 119297
negative_passages.text: Finding invertible polynomials in polynomial ring $\mathbb{Z}_{n}[x]$
negative_passages.docid: 100340
negative_passages.text: Invariant dimension property on a ring without zero divisors
negative_passages.docid: 102464
negative_passages.text: Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
negative_passages.docid: 74441
negative_passages.text: Zero divisors in matrix rings
negative_passages.docid: 112099
negative_passages.text: Polynomial ring with integral coefficients is integral
negative_passages.docid: 23641
negative_passages.text: Quotient ring of field is zero or itself.
negative_passages.docid: 115541
negative_passages.text: Subrings of polynomial rings over the complex plane
negative_passages.docid: 111493
negative_passages.text: Division algorithm for polynomials in R[x], where R is a commutative ring with unity.