【摘要】 令Λ为一个Artin代数,Γ为Λ的A-R箭图ΓΛ的一个分支,且Γ不包含有向循环。Size Li已经证明出以下事实:Γ能被嵌入到某个ZΔ中(其中Δ同构于Γ的一个截面,Z是整数集),当且仅当每一条可能的IP路为sectional路。利用这一定理,讨论几种满足一定条件的A-R分支的嵌入和截面的性质。更多还原

【Abstract】 Let Λ be an Artin algebra, Γ be a component of its A-R quiver Γ_Λ and Γ contains no oriented cycle. Size Li has proved theorem: Let Γ be a component of Γ_Λ containing no oriented cycle. Then Γ can be embedded in some ZΔ with Δ isomorphic to a section of Γ, if every possible path from an injective vertex to a projective vertex is sectional.The theorem is usesl to discuss the embedding of the components which satisfy some conditions. A property of section is also provided.更多还原