剩余格蕴涵代数中n-重素滤子的研究

The n-fold Prime Filter of Residuated Lattice Implication Algebras

在剩余格蕴涵代数中,提出了n-重素滤子的概念,并研究了它的性质.讨论了n-重素滤子与关联滤子、n-重素滤子与素滤子、n-重素滤子与准素滤子和对不同的自然数n,n-重素滤子之间的关系.最后,得到了在格H蕴涵代数中,n-重素滤子与素滤子等价和n-重素滤子与准素滤子等价的结论.

The concept of n-fold prime filter is proposed in residuated lattice implication algebras,and then its property is researched.The relations between n-fold prime filter and implicative filter,n-fold prime filter and prime filter,n-fold prime filter and primary filter,etc.,are discussed.Finally,the conclusions that an n-fold prime filter is equivalent to a prime filter and a primary filter are proved respectively in lattice H implication algebras.