R_0-代数的理想与其定义的简化

Ideas and reduced definitions of R_0-algebras

为了建立R0 代数的理想和同余之间的关系和简化它的原始定义,首先给出了R0 代数的若干基本性质,然后证明了R0 代数的理想之集与R0 代数上的同余关系之间,以及R0 代数的特殊理想之集与商R0 代数的理想之集之间分别存在一一对应关系.结果表明,R0 代数的原始定义中的逆序对合对应与分配性是不独立的,从而简化了R0 代数的定义.

In order to establish relation between its ideas and congruencies, the elementary properties of an R_0-algebra were given firstly. Then it is proved that there exists a bisection between the set of ideas and that of congruences and between the set of certain ideas and that of ideas of the quotient algebra for any R_0-algebra, respectively. Finally it is found that the order-reversing involution correspondence and distributivity in the initial definition are not independent, which leads to the reduced definition.