query: Elements in a commutative ring ( Zero divisors , Unit)
positive_passages.docid: 14343
positive_passages.text: Every nonzero element in a finite ring is either a unit or a zero divisor
negative_passages.docid: 83115
negative_passages.text: A set of elements in a reduced unity ring
negative_passages.docid: 37960
negative_passages.text: Zero Divisors in Direct Product of Rings
negative_passages.docid: 22563
negative_passages.text: Units and Nilpotents
negative_passages.docid: 80088
negative_passages.text: What possible characteristics may a local commutative unital ring have?
negative_passages.docid: 16023
negative_passages.text: Are associates unit multiples in a commutative ring with $1$?
negative_passages.docid: 114254
negative_passages.text: Zero divisors in $A[x_1,x_2,\dots,x_r]$
negative_passages.docid: 20613
negative_passages.text: Units (invertibles) of polynomial rings over a field
negative_passages.docid: 92420
negative_passages.text: Characteristic of  a Non-unital Integral Ring
negative_passages.docid: 1576
negative_passages.text: Finding the elements in the group of units of the ring of integers modulo n that are their own inverse.
negative_passages.docid: 81743
negative_passages.text: Prime ideals in $C[0,1]$
negative_passages.docid: 155445
negative_passages.text: What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$
negative_passages.docid: 69012
negative_passages.text: How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
negative_passages.docid: 68807
negative_passages.text: How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
negative_passages.docid: 130814
negative_passages.text: Quotient of semi-simple rings
negative_passages.docid: 74441
negative_passages.text: Zero divisors in matrix rings