Almost Split Sequences in Dimension One (original) (raw)

Communications in Algebra, 2010

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.

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