On Heller lattices over ramified extended orders

Let O be a complete discrete valuation ring with unique maximal ideal (π) and residue class field k=O/(π), and let Λ be an O-order. Λ¯ denotes the k-algebra Λ/πΛ. In this paper, we study Heller lattices of Λ¯-modules and investigate sufficient conditions of their indecomposability (Theorem 2.9). Also, we show that some short exact sequences of Λ¯-modules are, modulo direct summands of split sequences, liftable to short exact sequences of Λ-lattices (Theorem 3.2). In the final section, we shall apply our results on orders to the group ring Λ=OG of a finite group G over O (Theorem 4.4).