Shod Algebras And The Hook In The IP Path

Representation theory of algebra is a new branch of algebra started in early 70's in last century.Its basic content is to study the structure of rings and algebras.In the last thirty years,this theory has got a great development and maturates gradually.Its main research is to study whether a given Artin algebra is representation-finite or not. If it is infinite,we show the distribution of modules;If it is finite,find its all indecomposable modules and classify algebras according to the relationship between indecomposable modules and AR-quiver.AR-quiver is the basic geometry shape of the module categories which in the algebras system.The almost split sequence is the foundation and the core of the Auslander-Reiten theory,which is the basic function in the representation theory of algebras but plays an important role in the representation theory of algebras.Over the years,there is a great development about the representation theory of algebras. D.Happel and C.Ringel introduced the tilted algebras as a generalization of hereditary algebras. The class of tilted algebras[l]is now considered to be one of the most useful algebras.One method to develop this theory is to start from a class of algebras whose representation theory is closed to the preceding class;by this way ,quasi-tilted algebras[2] and small homological dimension algebras[3] were introduced according to hereditary algebras and tilted algebras.In this paper we introduce some new conclusions about shod algebras and give the classification related to the IP path in the AR-quiver,meanwhile we introduce the characters of the IP path in the strict shod algebras.