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Irreducible homomorphisms for lattices over orders

Published online by Cambridge University Press:  17 April 2009

Joachim W. Schmidt
Joachim W. Schmidt*
Affiliation:
Mathematisches Institut der Universität, Stuttgart, Bundesrepublik Deutschland.
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Abstract

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Let Λ be a complete R-order in the semi-simple K-algebra A. Then it has been shown that for each indecomposable Λ-lattice M which is not projective, there exists a unique almost split sequence 0 → N → E → M → 0. Here we study the middle term E and characterize those almost split sequences where E has a projective direct summand. In the case where Λ is the group-ring RG for a finite group G, we get information about the almost split sequences for the syzygies and apply our results in an example.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 1 , August 1977 , pp. 109 - 124
Copyright
Copyright © Australian Mathematical Society 1977

References

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