Almost Split Sequences in Dimension One

Abstract

Let R be a complete discrete valuation ring with quotient field K, and let Λ be an R-order in a semisimple K-algebra. For an indecomposable Λ-lattice E, a sublattice Bi E satisfying Rad E ⊂ Bi E is defined, and it is shown that the middle term H of an almost split sequence τE ↣ H ↠ E can be obtained by an amalgamation of E/Bi E with E′/τE for a suitable overlattice E′ of τE. The method is bound to dim R = 1.

Key Words:

• Almost split sequence
• Cohen–Macaulay order

2000 Mathematics Subject Classification:

• Primary 16G30, 16G70

Notes

Communicated by S. Goto.