群上的软同余关系

Soft Congruence Relations on Groups

引入了半群、群及软群上的软同余关系,并定义了半群上的软商集、群上的软陪集及软陪集下的软商集,讨论了半群上的软同余与同态、软同态之间的联系,同时得到群和软群上软同余的一系列相关结果,进一步揭示了软同余和正规化软群、正规软子群之间的关系。

In this paper, the concepts of soft congruence relations over semigroups, groups and soft groups are introduced. Also, the definitions of soft quotient set over semigroup, soft coset over group and soft quotient set over soft coset are given. The basic aim of this paper is to discuss connections among soft congruence relations and homomorphisms, soft homomorphisms over semigroups. At the same time, some relative results on soft congruence relations over groups and soft groups are obtained, which reveals the connections among soft congruence relations and normalistic soft groups, normal soft subgroups.