差半环的结构  

Construction of Difference Semirings

作　　者：欧启通[1] 

机构地区：[1]厦门理工学院数理系,福建厦门361024

出　　处：《西南师范大学学报（自然科学版）》2010年第5期9-13,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：福建省自然科学基金资助项目(Z0511050);福建省教育厅自然科学基金资助项目(JA06047);厦门理工学院科技基金资助项目

摘　　要：借助泛代数的思想方法,引入了半环上两类同余概念.在此基础上,提出了半环的两类差半环的概念,讨论了两类差半环的性质,证明了半环上的所有加法可消弱同余之集关于集合的包含关系构成完全格.同时,得到了两类差半环的结构.By using the method of universal algebra,the concepts of two classes of congruences over a semiring are introduced.Then the concepts of two classes of difference semirings of a semiring are proposed,several elementary properties of difference semirings are discussed.It is proved that the set of all additive cancellable weak congruences over a semiring forms a complete lattice with respect to the partial order of set inclusion.Finally the construction of difference semirings is obtained.

关 键 词：半环 理想 强同余 弱同余 差半环 

分 类 号：O153.3[理学—数学]