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On the construction of ring extensions

Published online by Cambridge University Press:  18 May 2009

Edward L. Green  and
Idun Reiten
Edward L. Green
Affiliation:
Department of MathematicsUniversity of PennsylvaniaPhiladelphia 19104
Idun Reiten
Affiliation:
Department of MathematicsUniversity of Trondheim7000 TrondheimNorway
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Let ∧ denote a basic artin ring and r its radical. In most of this paper we assume that r2 = 0 and that Λ is a trivial extension Λ/r ⋉ r (see Section 1 for definition). Let P1 …, Pn be the non-isomorphic indecomposable projective (left) Λ-modules, and consider triples (Pi, Mi, ui), where the Mi, are (left) Λ-modules and ui:rPi → Mi/rMi isomorphisms. From this data we construct a new ring Г, which in “nice cases” has the property that r′3 = 0, Г/r′2 ≅ Λ, and r′ Qi ≅ Mi as (left) Λ-modules, where the Qi are the indecomposable projective (left) Г-modules and r′ is the radical of Г.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 1 , January 1976 , pp. 1 - 11
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

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