带有IP路的shod代数

Shod Algebra with IP-Path

结合Λ的箭图中的IP路给出了有限维代数的新结论:Λ是严格shod代数当且仅当indΛ中的任意IP路都可以提升成一条路IP,且一定存在包含钩子IP的路,这条IP路中要么有一个钩子,要么有两个连续的钩子.

An algebra A is shod if for each indecomposable module X, either its projective dimension is at most one. The main conclusion of this article is that A is a strict shod algebra if and only if any IP -path in indA can be refined to be a →↑IP -path, and there exists →↑IP -path containing one hook or two consecutive hooks.