On Degenerations and Splitting of Exact Sequences

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.

Key Words:

• Degeneration
• Modules
• Representation type
• Split

Mathematics Subject Classification:

• Primary 16G60, 14D06
• Secondary 13E10

Notes

^#Communicated by S. Goto.