On the construction of ring extensions
- 1 January 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 17 (1) , 1-11
- https://doi.org/10.1017/s0017089500002640
Abstract
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.This publication has 4 references indexed in Scilit:
- Trivial Extensions of Abelian CategoriesLecture Notes in Mathematics, 1975
- Pathological quasi-frobenius algebras of finite typeCommunications in Algebra, 1974
- Unzerlegbare Darstellungen Imanuscripta mathematica, 1972
- On the Dimension of Modules and Algebras, IV: Dimension of Residue Rings of Hereditary RingsNagoya Mathematical Journal, 1956