Abstract
We generalize the notion of degenerations to any modules over general rings and we show basic properties and characterization of degenerations still hold under our definition. We also study the splitting of short exact sequences of the form 0 → M → M ⊕ M → M → 0. We show that the splitting of these exact sequences characterizes the representation type (i.e., finite type or infinite type) of artin algebras.
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#Communicated by S. Goto.