query: Principal ideals and units
positive_passages.docid: 16023
positive_passages.text: Are associates unit multiples in a commutative ring with $1$?
negative_passages.docid: 75899
negative_passages.text: Principal ideal domain with finitely many ideals
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: 18186
negative_passages.text: Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
negative_passages.docid: 41629
negative_passages.text: Structure of ideals in the product of two rings
negative_passages.docid: 60223
negative_passages.text: Two principal ideals coincide if and only if their generators are associated
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 16945
negative_passages.text: Finding the Ideals of a Direct Product of Rings
negative_passages.docid: 114193
negative_passages.text: On the absolute norm of an ideal
negative_passages.docid: 1719
negative_passages.text: Ideals in the ring of Gaussian integers
negative_passages.docid: 148550
negative_passages.text: Units in quotient ring of $\mathbb Z[X]$
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.
negative_passages.docid: 93929
negative_passages.text: The height of a principal prime ideal
negative_passages.docid: 94157
negative_passages.text: Normal Ring and Prime Ideal whose Square is Principal
negative_passages.docid: 119056
negative_passages.text: If in a UFD every maximal ideal is principal then it is a PID
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$
negative_passages.docid: 20877
negative_passages.text: The set of all nilpotent elements is an ideal