正则FI-代数上的伴随算子

On the adjoint operators of regular FI-algebras

研究了正则FI 代数的性质,并证明了对于正则FI 代数(L,→,0)的蕴涵算子→,存在惟一满足条件(a b)→c=a→(b→c)的算子 ,使得( ,→)成为伴随对.所得结果在一定程度上反映了正则剩余格内部结构的特征.

The regular FI-algebras are further studied because of their wide applications in logic systems, the new properties of regular FI-algebras are obtained. Moreover, it is proved that if (L,→,0) is a regular FI-algebra then there is the unique implicaton operator  such that(,→) to become an adjoint couple on L satisfying the condition (ab)→c=a→(b→c). These results may describe the characterizations of interior structures of the regular FI-algebras.