Fuzzy prime Boolean filters and their operations in IMT L-algebras |
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| Authors: | Jia-lu Zhang |
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| Institution: | (1) Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, People’s Republic of China;(2) Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 610031, People’s Republic of China; |
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| Abstract: | Some characterizations of fuzzy prime Boolean filters of IMT L-algebras are given. The lattice operations and the order-reversing involution on the set PB(M) of all fuzzy prime Boolean filters of IMT L-algebras are defined. It is showed that the set PB(M) endowed with these operations is a complete quasi-Boolean algebra (a distributive complete lattice with an order-reversing
involution). It is derived that the algebra M=F, which is the set of all cosets of F, is isomorphic to the Boolean algebra {0; 1} if F is a fuzzy prime Boolean filter. By introducing an adjoint pair on PB(M), it is proved that the set PB(M) is also a residuated lattice. |
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