query: Proof of: if A is an integral domain, then the units of A[x] are the constant polynomials that are units of A
positive_passages.docid: 35222
positive_passages.text: Characterizing units in polynomial rings
negative_passages.docid: 94819
negative_passages.text: Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
negative_passages.docid: 52966
negative_passages.text: Rings, ideals and units-proof
negative_passages.docid: 71479
negative_passages.text: Is there some elementary proof of invariance of domain?
negative_passages.docid: 80397
negative_passages.text: Show that this set of polynomials is ideal in F[x]
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 101637
negative_passages.text: Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
negative_passages.docid: 99737
negative_passages.text: Using Rouché's theorem to find a compact domain for the roots of a polynomial
negative_passages.docid: 7011
negative_passages.text: Integral domain with fraction field equal to $\mathbb{R}$
negative_passages.docid: 134458
negative_passages.text: Isomorphisms preserving integral domains and fields
negative_passages.docid: 47474
negative_passages.text: Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
negative_passages.docid: 1580
negative_passages.text: An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal
negative_passages.docid: 138114
negative_passages.text: Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
negative_passages.docid: 81982
negative_passages.text: Is $\mathbb{Z}[x]$ a principal ideal domain?
negative_passages.docid: 71799
negative_passages.text: A complex polynomial with partial derivatives equal to zero is constant.
negative_passages.docid: 20613
negative_passages.text: Units (invertibles) of polynomial rings over a field
negative_passages.docid: 132193
negative_passages.text: Why $\Bbb Z$ = (integers) is an integral domain?