弱幻方的代数系统

The Algebraic System of Weak Magic Squares

在弱幻方定义的基础上,采用类比法研究了相关代数系统,从而结合抽象代数的相关定义提出弱幻方关于二元运算■和■的代数系统:弱和幻方关于■构成代数系统、半群、交换半群、群、交换群;弱积幻方关于■构成代数系统、半群、有幺元的交换半群;弱和弱积幻方关于■和■构成代数系统、环。

Based on the definition of weak magic square,the system of correlative algebra is studied by analogy.And then combined with the definition of abstract algebra,the algebraic system of the weak magic squares about two operations ■ and ■ is put forward:weak sum of magic square about ■ operation constitute algebraic system,semigroups,commutative semigroups,groups,commutative groups;weak product of magic square about ■ operation constitute algebraic system,semigroups,commutative semigroups constituting unite;The weak sum and weak pruduct of magic square constitute algebraic systems and rings with respect to and ■.