On tense modules for extended algebras over rational fields
Let k(x) be the field of fractions of the polynomial algebra k[x] over the field k. We prove that, for an arbitrary finite dimensional k-algebra Λ, any finitely generated Λ ⊗ k k(x)-module M such that its minimal projective presentation admits no non-trivial selfextension is of the form M ≅ Nk(x), for some finitely generated Λ-module N. Some consequences are derived for tilting modules over the rational algebra Λ ⊗ k k(x) and for some generic modules for Λ.
Mathematics Subject Classification (2000).Primary 16A46 16A53 Secondary 15A21
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