关于半群上的GP-平坦系  

On GP-Flat S-Acts over Semigroups

作　　者：马维楷 MA Wei-kai(Alxa Vocational&Technical College,Alxa 750300,China)

机构地区：[1]内蒙古阿拉善职业技术学院,内蒙古阿拉善750300

出　　处：《数学的实践与认识》2024年第5期182-189,共8页Mathematics in Practice and Theory

摘　　要：半群的S-系理论是研究半群代数的一种有效方法,平坦系是该理论研究的重要对象之一.在半群的S-系范畴中引入平坦系的广义形式,称之为GP-平坦系,通过讨论S-系的GP-平坦性与直积、余直积和挠自由性的关系,给出GP-平坦系的基本性质,通过研究GP-平坦性质给出有局部单位半群的刻画,进而推广幺半群的已有重要结果.本研究对于揭示含幺半群理论与不含幺元半群理论的区别与联系,以及探索平坦性质在半群中的应用具有重要意义.The S-act theory for semigroups is recognized as an important theory in studying semigroups from the external action,and flat S-acts are important research objects in this theory.A general form of flat acts called GP-fat acts is introduced.By exploring the relationship between GP-flat acts and direct products(coproducts,torsion free acts),some basic properties of GP-flat acts are given.By investigating GP-flatness of acts,semigroups with local units are are characterized.Furthermore,many known results are generalized.This research will further apply the S-acts theory to semigroups.Meanwhile,it will have an important significance in revealing the differences and connections between semigroup theory and monoid theory,and exploring the application of fat acts in semigroup theory.

关 键 词：有局部单位半群 广义正则半群 S-系 主弱平坦系 GP-平坦系 

分 类 号：O152.7[理学—数学]