query: A finite ring without zero divisors is a division ring
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: 117777
negative_passages.text: What are the zero divisors of $C[0,1]$?
negative_passages.docid: 92420
negative_passages.text: Characteristic of  a Non-unital Integral Ring
negative_passages.docid: 130814
negative_passages.text: Quotient of semi-simple rings
negative_passages.docid: 74314
negative_passages.text: Noetherian ring and the same prime divisors
negative_passages.docid: 154530
negative_passages.text: Rings whose elements are partitioned between units and zero-divisors.
negative_passages.docid: 93474
negative_passages.text: A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$
negative_passages.docid: 102072
negative_passages.text: Simple $M_n(D)$-module with $D$ a division ring
negative_passages.docid: 143884
negative_passages.text: A non-noetherian ring with noetherian spectrum
negative_passages.docid: 125604
negative_passages.text: Proof that $\mathbb{Z}$ has no zero divisors
negative_passages.docid: 78350
negative_passages.text: When does a finite ring become a finite field?
negative_passages.docid: 112560
negative_passages.text: Simple Noetherian domain which is not a division ring
negative_passages.docid: 39049
negative_passages.text: Ring With Unity As a Direct Sum of Non-Zero Ideals
negative_passages.docid: 45484
negative_passages.text: Height unmixed ideal and a non-zero divisor
negative_passages.docid: 116000
negative_passages.text: Prove that prime ideals of a finite ring are maximal
negative_passages.docid: 131319
negative_passages.text: I understand what a division ring is, but cannot find any examples. Can anyone give me one?
negative_passages.docid: 11541
negative_passages.text: Examples of a non-commutative division ring