BL代数的fantastic滤子和normal滤子

On fantastic filters and normal filters of BL-algebras

滤子是研究逻辑代数的有效工具.本文研究了BL代数的fantastic和normal滤子的等价条件,得到了在MV-代数中两种滤子之间的等价性,给出了两个公开问题:"在什么样的合适条件下,一个normal滤子成为一个fantastic滤子?"和"在什么合适的条件下,normal滤子的拓展性成立?"结论成立的一种条件.

Filter is an effective tool to study of the logic algebras. We study the equivalent conditions of fantastic filter and normal filter in BL-algebras, and we reveal the equivalence between fantastic filter and normal filter in MV-algebras and proposed a condition under which two open problems hold that ＂Under what suitable condition a normal filter becomes a fantastic filter？＂ and ＂（Extension property for a normal filter） Under what suitable condition extension property for normal filter holds？＂.