noetherian module 中文意思是什麼
noetherian module
解釋
諾特模- module : n. 1. 測量流水等的單位〈1秒100升〉。2. 【建築】圓柱下部半徑度。3. 【物理學】模，系數，模數，模量。4. 【無線電】微型組件；組件；模塊。5. （太空船上各個獨立的）艙。
-
At first a lot of new characterizations of gorenstein injective modules are given, then the author claim that a ring r is qf if and only if every left ( or right ) r - modules are gorenstein injective, and then show that if r is two - side noetherian, r is n - gorenstein if and only if every n - th cosyzygy of an injective resolution of a left ( and right ) r - module is gorenstein injective if and only if every n - th syzygy of an injective resolvent of a left ( and right ) right module is gorenstein injective. finally, we prove that for an n - gorenstein ring r with n > 0, every module can be embedded in a gorenstein injective module and the injective dimension of its cokernel is at most n - 1
首先給出了gorenstein內射模的許多新的刻畫，推出了環r是qf環當且僅當每個左（右）的r -模的單邊內射分解式的第n個上合沖是gorenstein內射模，接著推出了左、右noether環只是n - gorenstein環當且僅當每個左（右）模的單邊內射分解式的第n個上合沖是gorenstein內射模當且僅當每個左（右）模的單邊內射預解式的第n合沖是gorenstein內射模，最後推出了n - gorenstein環中每個模都可嵌入到一個gorenstein內射模之中，且其上核的內射維數不大於n - 1 。
分享友人