【摘要】：文章給出了軟交半群、軟交Clifford半群、軟交子Clifford半群、軟卷積代數和軟卷積限制子代數的概念,研究了它們的一些相關性質和判定準則,并討論了冪等軟卷積代數的一些等價條件。以下為主要內容和相關結論:第三章中,給出了軟交半群、軟交Clifford半群和軟交子Clifford半群的概念,并討論了它們的一些性質。此外,還研究了軟交Clifford半群的判定定理。第四章中,給出了軟卷積代數和軟卷積限制子代數的概念,得到有關軟卷積代數交換性的等價刻畫,并研究了軟卷積代數在結合律和分配律方面的運算性質,最后給出軟卷積代數中單位元的判定準則。第五章中,研究了二元關系“?”在軟卷積代數中的傳遞性,討論了它的一些性質。其次,給出軟卷積代數和軟卷積限制子代數在不同運算中關于交換性及冪等性的等價刻畫,并得到相關結論。
[Abstract]:In this paper, the concepts of soft intersection Semigroups, soft intersection Clifford Semigroups, soft intersection subgroups Clifford Semigroups, soft convolution algebras and soft convolution restricted subalgebras are given. Some equivalent conditions of idempotent soft convolution algebra are discussed. The following are the main contents and related conclusions: in chapter 3, we give the concepts of soft intersecting Semigroups, soft intersecting Clifford Semigroups and soft crossover subgroups Clifford Semigroups, and discuss their properties. In addition, the decision theorem of soft intersection Clifford semigroup is studied. In chapter 4, the concepts of soft convolution algebra and soft convolution restricted subalgebra are given, and the equivalent characterizations of commutativity of soft convolution algebra are obtained, and the computational properties of soft convolution algebra in terms of associative law and distribution law are studied. Finally, the criterion of unit element in soft convolution algebra is given. In the fifth chapter, we study the duality relation. Some properties of transitivity in soft convolution algebra are discussed. Secondly, the equivalent characterizations of commutativity and idempotent of soft convolution algebras and soft convolution restricted subalgebras in different operations are given, and the relevant conclusions are obtained.
【學位授予單位】：江南大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O159;O152.7

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