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A counterexample to Raikov's conjecture
Author(s) -
Rump Wolfgang
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn080
Subject(s) - counterexample , mathematics , conjecture , abelian group , construct (python library) , pure mathematics , class (philosophy) , property (philosophy) , type (biology) , algebra over a field , discrete mathematics , computer science , epistemology , artificial intelligence , ecology , philosophy , biology , programming language
Quasi‐abelian categories are additive categories for which the class of all short exact sequences defines an exact structure. Such categories are ubiquitous and form a natural framework for relative homological algebra and K ‐theory. Higher Ext‐groups also exist in categories with the formally weaker property to be semi‐abelian. Raikov's conjecture states that both concepts are equivalent. We use a tilted algebra of type 6 to construct a counterexample.