摘要
证明了左R-模M是内射的当且仅当分次左R-模M是gr-内射的,当且仅当分次左R-模M是gr-内射的;左R-模M是Noether的当且仅当分次左R[x]-模M[x]是gr-Noether的,当且仅当分次左R[x]-模M[x]是Noether的;左R-模M是Artin的当且仅当分次左R[x]-模M[x]是gr-Artin的,当且仅当分次左R[x]-模M[x]是Artin的;双模RMS定义了一个拟对偶当且仅当分次双模R[x]M[x-1]S[x]定义了一个gr-拟对偶.
Proves the following result:A left R
module M is injective if and only if the graded left R module is gr injective
if and only if graded left R module M is gr injective. A left R module M is
Noetherian (Artinian) if and only if the graded left R module M is gr Noetherian
(Artinian).An (R,S) bimodule RM S defines a quasi duality if and only if graded
(R,S) bimodule R M[x -1 ] S defines a gr quasi duality.
出处
《福建师范大学学报(自然科学版)》
CAS
CSCD
1999年第1期1-6,共6页
Journal of Fujian Normal University:Natural Science Edition
基金
福建省自然科学基金