滤子软偏序半群研究  

Study on filter soft partially ordered semigroups

作　　者：邵海琴[1] 梁茂林[1] 何建伟[1] SHAO Haiqin;LIANG Maolin;HE Jianwei(School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,Gansu Province,China)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《浙江大学学报（理学版）》2023年第5期521-526,共6页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11961057);天水师范学院校级一般项目(JY203008).

摘　　要：将软集合理论应用于偏序半群。首先,引入偏序半群S上的左(右)滤子软偏序半群、滤子软偏序半群、完全左(右)滤子软偏序半群、完全滤子软偏序半群、素左(右)理想软偏序半群和素理想软偏序半群概念。其次,利用素左(右)理想软偏序半群和素理想软偏序半群,分别给出了S上的一个非空软集合是右(左)滤子软偏序半群和滤子软偏序半群的充分必要条件。最后,研究了S上的左(右)滤子软偏序半群、滤子软偏序半群、完全左(右)滤子软偏序半群和完全滤子软偏序半群的商序同态像和在偏序同态映射下的逆像,得到了一些相关结论。In this paper,we apply the theory of soft sets to partially ordered semigroup.First,several new notions such as left(right)filter soft partially ordered semigroup,filter soft partially ordered semigroup,whole left(right)filter soft partially ordered semigroup,whole filter soft partially ordered semigroup,prime left(right)ideal soft partially ordered semigroup,prime ideal soft partially ordered semigroup over partially ordered semigroups S are introduced.Further,with prime left(right)ideal soft partially ordered semigroup and prime ideal soft partially ordered semigroup over S,the necessary and sufficient conditions that the non-null soft set over S is a right(left)filter soft partially ordered semigroup and filter soft partially ordered semigroup over S are given separately.Finally,quotient ordered homomorphic images and inverse images under partially ordered homomorphic on left(right)filter soft partially ordered semigroup,filter soft partially ordered semigroup,whole left(right)filter soft partially ordered semigroup and whole filter soft partially ordered semigroup are studied,and some related conclusions are obtained.

关 键 词：偏序半群 滤子软偏序半群 完全滤子软偏序半群 素理想软偏序半群 偏序同态 商序同态 

分 类 号：O152.7[理学—数学]