query: What are the invertible elements of the $K[X]$ ring where $K$ is a field?
positive_passages.docid: 20613
positive_passages.text: Units (invertibles) of polynomial rings over a field
negative_passages.docid: 16643
negative_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 31142
negative_passages.text: Why does $K \leadsto K(X)$ preserve the degree of field extensions?
negative_passages.docid: 60212
negative_passages.text: algebraic element over a field
negative_passages.docid: 30327
negative_passages.text: $\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
negative_passages.docid: 7303
negative_passages.text: How many idempotent elements does the ring ${\bf Z}_n$ contain?
negative_passages.docid: 8787
negative_passages.text: In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
negative_passages.docid: 78561
negative_passages.text: Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
negative_passages.docid: 117005
negative_passages.text: Rules in the ring with coefficients in finite field $\mathbb{F}_p$
negative_passages.docid: 143051
negative_passages.text: Inverting noninvertible elements in a bigger ring.
negative_passages.docid: 21946
negative_passages.text: What do prime ideals in $k[x,y]$ look like?
negative_passages.docid: 85987
negative_passages.text: Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
negative_passages.docid: 120557
negative_passages.text: Group of invertible elements of a ring has never order $5$
negative_passages.docid: 119067
negative_passages.text: Basic Ring Theory Question involving the unit element
negative_passages.docid: 80961
negative_passages.text: Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
negative_passages.docid: 143429
negative_passages.text: Kernel of ring homomorphism $k[X,Y] \rightarrow k[t^2, t^3]$
negative_passages.docid: 14055
negative_passages.text: How to show that a finite commutative ring without zero divisors is a field?