关于半群上的GP-平坦系
On GP-Flat S-Acts over Semigroups
马维楷1
作者信息
- 1. 内蒙古阿拉善职业技术学院,内蒙古 阿拉善 750300
- 折叠
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.
Abstract
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-flat 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 flat 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Key words
semigroups with local units/generally regular semigroups/S-acts/principally weakly flat acts/GP-flat acts引用本文复制引用
出版年
2024
NETL
NSTL
万方数据