论文标题
Auslander-Reiten和Huneke-Wiegand猜想了准纤维产品环
Auslander-Reiten and Huneke-Wiegand conjectures over quasi-fiber product rings
论文作者
论文摘要
在本文中，我们探讨了在准纤维产品环上有限生成的模块$ r $ $ {\ rm ext} $消失的后果；也就是说，$ r $是本地环，因此$ r/（\ usevenline x）$是一种非平凡的光纤产品环，对于某些常规序列$ \ $ \ $ r $的X $。同等地，$ r/（\下划线x）$的最大理想是将两个非零理想的直接总和分解。 Gorenstein准纤维产品环是AB环，并且延伸。我们在定理3.31中显示准纤维产物环满足了Auslander-Reiten猜想的锐化形式。我们还对准纤维产品环的Huneke-Wiegand猜想进行了一些观察。
In this paper we explore consequences of the vanishing of ${\rm Ext}$ for finitely generated modules over a quasi-fiber product ring $R$; that is, $R$ is a local ring such that $R/(\underline x)$ is a non-trivial fiber product ring, for some regular sequence $\underline x$ of $R$. Equivalently, the maximal ideal of $R/(\underline x)$ decomposes as a direct sum of two nonzero ideals. Gorenstein quasi-fiber product rings are AB-rings and are Ext-bounded. We show in Theorem 3.31 that quasi-fiber product rings satisfy a sharpened form of the Auslander-Reiten Conjecture. We also make some observations related to the Huneke-Wiegand conjecture for quasi-fiber product rings.
