Multi-folded <i>N</i>-Structures with Finite Degree and its Application in BCH-Algebras

Abstract

The generalization of N-structure is introduced first and then applied to BCH-algebra for research. The concepts of k-folded N-subalgebra, k-folded N-dosed ideal and (closed) k-folded N-filter are introduced, and then their relations and several properties are investigated. Conditions for the k-folded N-subalgebra to be k-folded N-closed ideal are provided. Characterization of k-folded N-subalgebra, k-folded N-closed ideal and (closed) k-folded N-filter are considered by using the notion of k-folded level sets. A k-folded N-subalgebra and a k-folded N-closed ideal are constructed by using the medial part and BCA-part. A k-folded N-filter is made by using the branch of a BCH-algebra. Conditions for a k-folded N-closed ideal to be a closed k-folded N-filter are discussed. (C) 2021 The Authors. Published by Atlantis Press B.V.