半环的粗糙理想  

Rough Ideals in Semirings

作　　者：段海婷[1] 邵勇[1] 胡静[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《广西民族大学学报（自然科学版）》2009年第1期33-36,共4页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：国家自然科学基金(10471112);陕西省教育厅自然科学专项基金(07JK413)

摘　　要：文[1]研究了半群中的理想,首次提出了粗糙半群和粗糙理想的概念.文章引进半环的粗糙左(右,双侧,拟,双)理想的概念,给出半环的左(右,双侧,拟,双)理想,就是半环的粗糙左(右,双侧,拟,双)理想,还研究了半环中两个理想做某种运算后的粗糙性质,进一步补充完善了粗糙集理论.Rough ideals in semigroups has been studied and first been introduced the concepts of rough semigroups and rough ideals in [1]. In this paper, we will introduce the concepts of rough left（right, two-side） ideal , rough quasi--ideal and rough bi--ideal in semirings, give that the left（right, two--side） ideal , quasi--ideal and bi--ideal in semirings is the rough left（right, two--side） ideal , rough quasi--ideal and rough bi--ideal in semirings, and also consider the rough propositions of two ideals maked some of operations in semiring, so the rough theory is completed and perfected.

关 键 词：半环 粗糙左(右 双侧)理想 粗糙拟理想 粗糙双理想 

分 类 号：O159[理学—数学]