Ideal and Filter Construction of Double Pseudo-Complement Ockham Algebras
The theory of order algebra has been widely used in theoretical computer,multi-valued logic,infor-mation system science and so on.In the field of ordered algebra,ideal and filter are important tools to describe the structure of algebras.Double pseudo-complement Ockham algebras are a new class of algebras defined on the basis of double pseudo-complement algebras and Ockham algebras.Based on the operation rules of double pseudo-complement Ockham algebras and the correlation between double pseudo-complement Ockham algebras,the ideals and filters of double pseudo-complement Ockham algebras are further studied.Firstly,filters of double pseudo-complement Ockham algebras are constructed by the operation of Ockham algebras,and the related properties are discussed.Secondly,by means of sufficient and necessary conditions of double pseudo-complement Ockham alge-braic kernel ideal and cokernel filter,the concrete set form of kernel ideal and cokernel filter is constructed.The re-sults will provide a method for the study of the ideal and filter properties of other order algebras,and will be helpful to further explore the application of order algebra theory in other disciplines such as fuzzy sets and computer sci-ence.
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