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The Gabriel–Roiter measure for radical‐square zero algebras
Author(s) -
Chen Bo
Publication year - 2009
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/bdn091
Subject(s) - mathematics , functor , algebraically closed field , zero (linguistics) , partition (number theory) , equivalence (formal languages) , pure mathematics , measure (data warehouse) , square (algebra) , algebra over a field , discrete mathematics , combinatorics , geometry , philosophy , linguistics , database , computer science
Let Λ be a radical‐square zero algebra over an algebraically closed field k with radical , and let Γ = (Λ / τ0τΛ / τ)be the associated hereditary algebra. There is an explicit functor F : mod Λ → mod Γ, which induces a stable equivalence. In this paper, it will be proved that the functor F preserves the Gabriel–Roiter (GR) measures and the GR factors. Thus the GR measure for Λ can be studied by the use of F and known facts for hereditary algebras. In particular, the middle terms of the Auslander–Reiten sequences ending at the GR factors and the relationship between the preprojective partition for Λ and the take‐off Λ‐modules will be investigated.