Geodesic
On the construction of ring extensions
Glasgow mathematical journal, Tome 17 (1976) no. 1, pp. 1-11

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Green, Edward L.; Reiten, Idun. On the construction of ring extensions. Glasgow mathematical journal, Tome 17 (1976) no. 1, pp. 1-11. doi: 10.1017/S0017089500002640
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