query: Example of a ring for which $rs \neq 0$ but $sr = 0$.
positive_passages.docid: 19838
positive_passages.text: Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
negative_passages.docid: 23641
negative_passages.text: Quotient ring of field is zero or itself.
negative_passages.docid: 39576
negative_passages.text: Quotient ring being isomorphic to the initial ring
negative_passages.docid: 74559
negative_passages.text: $A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
negative_passages.docid: 72507
negative_passages.text: Does $ab=1$ imply $ba=1$ in a ring?
negative_passages.docid: 11573
negative_passages.text: Rings and some of their properties
negative_passages.docid: 63192
negative_passages.text: A chain ring with Krull dimension greater than one
negative_passages.docid: 76749
negative_passages.text: Example of a finite non-commutative ring without a unity
negative_passages.docid: 37960
negative_passages.text: Zero Divisors in Direct Product of Rings
negative_passages.docid: 11541
negative_passages.text: Examples of a non-commutative division ring
negative_passages.docid: 82953
negative_passages.text: In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
negative_passages.docid: 157266
negative_passages.text: Can a nonzero polynomial evaluate to the zero function in a suitable infinite ring of char 0?
negative_passages.docid: 101095
negative_passages.text: Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
negative_passages.docid: 102316
negative_passages.text: why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
negative_passages.docid: 111679
negative_passages.text: Example of a ring without unity that has a subring with unity?
negative_passages.docid: 40014
negative_passages.text: A polynomial that is zero on an open set
negative_passages.docid: 100340
negative_passages.text: Invariant dimension property on a ring without zero divisors