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Pure Mathematics 2024
Clifford半群上的罗巴算子
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Abstract:
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。
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.
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