query: If $\{f_i\}$ generate the unit ideal in a ring, so do $\{f_i^N\}$ for any positive $N$
positive_passages.docid: 92822
positive_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 68202
negative_passages.text: Must an ideal generated by an irreducible element be a maximal ideal?
negative_passages.docid: 146304
negative_passages.text: prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
negative_passages.docid: 464
negative_passages.text: Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
negative_passages.docid: 34183
negative_passages.text: An equivalent condition with $\{0\}$ being the only nilpotent ideal
negative_passages.docid: 112150
negative_passages.text: Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
negative_passages.docid: 74537
negative_passages.text: Maximal Ideals in $K[y]$
negative_passages.docid: 96144
negative_passages.text: Every element outside the maximal ideal of a local ring is a unit
negative_passages.docid: 52966
negative_passages.text: Rings, ideals and units-proof
negative_passages.docid: 107454
negative_passages.text: Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
negative_passages.docid: 36150
negative_passages.text: Ideal in a ring of continuous functions
negative_passages.docid: 89864
negative_passages.text: Units in finite polynomial rings
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$
negative_passages.docid: 99423
negative_passages.text: Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?
negative_passages.docid: 29019
negative_passages.text: Ideals in direct product of rings
negative_passages.docid: 114343
negative_passages.text: If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
negative_passages.docid: 43230
negative_passages.text: Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?