剩余格的弱布尔积表示

Weak Boolean Representation of Residuated Lattices

在剩余格L中,首先证明了因子同余是由布尔元所唯一生成的,继而证明了由B(L)的素滤子诱导的商代数是直不可分解的。其次,给出了剩余格L的弱布尔积表示,并证明了伴随表示的等价性。最后,证明了剩余格L的序素谱与其stalks的素谱基数和序同构。

Firstly,it is proved that the factor congruence is uniquely generated by Boolean elements in the residuated lattice L,and then it is proved that the quotient algebra induced by the prime filter is directly indecomposable.Secondly,the weak Boolean product representation of the residuated lattice L is given,and the equivalence of adjoint representation is proved.Finally,it is proved that the ordered prime spectrum of the residuated lattice L is isomorphic to the cardinal sum of the ordered prime spectra of its stallks.