%0 Journal Article
%T Clifford半群上的罗巴算子<br>Rota-Baxter Operators on Clifford Semigroups
%A 龚晓倩
%A 尹碟
%J Pure Mathematics
%P 590-598
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/pm.2024.145212
%X 代数上的罗巴算子的理论已有丰富的成果。2021年，Guo，Lang和Sheng提出了群上罗巴算子的概念。最近，作为群上罗巴算子的推广，Catino，Mazzotta和Stefanelli又提出了Clifford半群上的(权为1的)罗巴算子。本文首先给出了Clifford半群上罗巴算子的一些新性质和新构造方法，然后提出了Clifford半群上权为？1的罗巴算子的概念，证明了Clifford半群上的罗巴算子和权为？1的罗巴算子之间存在一一对应关系，推广了群上罗巴算子的相关结果。<br />
The theory of Rota-Baxter operators on algebras has been fruitful. In 2021, Guo, Lang and Sheng have introduced the notion of Rota-Baxter operators on groups. Recently, as a generalization of Rota-Baxter operators on groups, Catino, Mazzotta, and Stefanelli have proposed Rota-Baxter operators with weight 1 on Clifford semigroups. In this paper, we first give some new properties and construction methods of Rota-Baxter operators with weight 1 on Clifford semigroups, then propose the concept of Rota-Baxter operators with weight ？1 on Clifford semigroups, and prove that there is a one-to-one correspondence between Rota-Baxter operators of weight 1 and ？1 on Clifford semigroups. This extends the results of Rota-Baxter operators on groups.
%K Clifford半群，罗巴算子<br>Clifford Semigroups
%K Rota-Baxter Operators
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=88729