半群S-分次环与冲积R#S^＊  

Semigroup 5-Graded Ring and Smash Product R#S~*

作　　者：张子龙[1] 蔡炳苓[1] 刘淑霞[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050016

出　　处：《数学学报（中文版）》2004年第5期985-992,共8页Acta Mathematica Sinica：Chinese Series

基　　金：河北省自然科学基金资助项目(102132)

摘　　要：设S为任意半群,本文以S-集为基础,讨论了S-集分次模的一些性质并得到范畴(S,A,R)-gr的一个有限生成投射生成子集合;对于冲积R#S*,主要证明了在一定条件下, unital左R#S*-模范畴和分次R-模范畴是同构的.Let S be a semi-group. For a semi-group S-set, we discuss some properties of modules graded by 5-sets and present a collection of finitely generated projective generators for (S, A, R)-gr, the category consisting of the left R-modules graded by a 5-set A with degree preserving .R-linear maps for the morphisms. For the smash product R#S*, we mainly prove the category of unital left R#S*-module is isomorphic to the category of graded .R-module on certain conditions.

关 键 词：左(右)可消半群 半群S-集 A-分次模 

分 类 号：O153[理学—数学]