软卷积代数
发布时间：2018-11-13 12:08
【摘要】：文章给出了软交半群、软交Clifford半群、软交子Clifford半群、软卷积代数和软卷积限制子代数的概念,研究了它们的一些相关性质和判定准则,并讨论了幂等软卷积代数的一些等价条件。以下为主要内容和相关结论:第三章中,给出了软交半群、软交Clifford半群和软交子Clifford半群的概念,并讨论了它们的一些性质。此外,还研究了软交Clifford半群的判定定理。第四章中,给出了软卷积代数和软卷积限制子代数的概念,得到有关软卷积代数交换性的等价刻画,并研究了软卷积代数在结合律和分配律方面的运算性质,最后给出软卷积代数中单位元的判定准则。第五章中,研究了二元关系“?”在软卷积代数中的传递性,讨论了它的一些性质。其次,给出软卷积代数和软卷积限制子代数在不同运算中关于交换性及幂等性的等价刻画,并得到相关结论。
[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.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159;O152.7
[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.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159;O152.7
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