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arxiv: math/0403087 · v2 · submitted 2004-03-04 · 🧮 math.RT · math.RA

Is tame open?

classification 🧮 math.RT math.RA
keywords conjectureopentamealgebrabasic-wild-rankranktame-openwild
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Is tame open? No answer so far. One may pose the Tame-Open Conjecture: Tame is open. But how to support it? No effective way to date. In this note, the rank of a wild algebra is introduced. The Wild-Rank Conjecture, which implies the Tame-Open Conjecture, is formulated. The Wild-Rank Conjecture is improved to the Basic-Wild-Rank Conjecture. A covering criterion on the rank of a basic wild algebra is given, which can be effectively applied to verify the Basic-Wild-Rank Conjecture for concrete algebras. It makes all conjectures much reliable.

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