w-模的w-底座

The w-Socles of w-Modules

引入了w-模的w-底座的概念,举例说明了w-底座与底座是不同的2个概念.借助w-底座,证明了设M是w-模,M是w-Artin模当且仅当若A是M的非零GV-无挠的商模,则w-soc(A w)≠0且w-soc(A w)是有限个w-单模的直和.

In this paper,we introduce the notion of the w-socle of a w-module and give an example to illustrate that the w-socle and the socle are different.Moreover,in terms of w-socles,we prove that let M be a w-module and let A be a non-zero GV-torsion-free quotient module of M,then M is w-Artinian if and only if the w-socle of Aw is non-zero and is the direct sum of its finite w-simple submodules.