query: Counterexample, Matsumura Exercise 2.5
positive_passages.docid: 46843
positive_passages.text: A ring without the Invariant Basis Number property
negative_passages.docid: 98372
negative_passages.text: Proof of the principle of backwards induction
negative_passages.docid: 41418
negative_passages.text: $2+2 = 5$? error in proof
negative_passages.docid: 140962
negative_passages.text: Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
negative_passages.docid: 66708
negative_passages.text: Elementary isomorphism between $\operatorname{PSL}(2,5)$ and $A_5$
negative_passages.docid: 9204
negative_passages.text: Counterexamples to the avoidance lemma for arbitrary ideals
negative_passages.docid: 98634
negative_passages.text: What is a counterexample for If $x\in\overline{A},$ $x$ is not necessarily a limit of a sequence in $A$?
negative_passages.docid: 105233
negative_passages.text: Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
negative_passages.docid: 62917
negative_passages.text: Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
negative_passages.docid: 123132
negative_passages.text: Counterexample for a non-measurable function?
negative_passages.docid: 22842
negative_passages.text: The Interpretation of $|\psi|^2$ and the No-Clone Theorem
negative_passages.docid: 61387
negative_passages.text: Incorrect Solution for Problem 7 of Pinter's Book of Abstract Algebra, Chapter 2?
negative_passages.docid: 131385
negative_passages.text: How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
negative_passages.docid: 43350
negative_passages.text: Schwarz's Lemma exercise
negative_passages.docid: 77735
negative_passages.text: When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
negative_passages.docid: 28452
negative_passages.text: Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$
negative_passages.docid: 153100
negative_passages.text: A counterexample to "$k\mid n$ if and only if $k\mid n^2$"