\(\mathcal N\)-structures applied to closed ideals in BCH-algebras
Summary: The notions of \(\mathcal N\)-subalgebras and \(\mathcal N\)-closed ideals in BCH-algebras are introduced, and the relation between \(\mathcal N\)-subalgebras and \(\mathcal N\)-closed ideals is considered. Characterizations of \(\mathcal N\)-subalgebras and \(\mathcal N\)-closed ideals are provided. Using special subsets, \(\mathcal N\)-subalgebras and \(\mathcal N\)-closed ideals are constructed. A condition for an \(\mathcal N\)-subalgebra to be an \(\mathcal N\)-closed ideal is discussed. Given an \(\mathcal N\)-structure, the greatest \(\mathcal N\)-closed ideal which is contained in the \(\mathcal N\)-structure is established.
scientific article; zbMATH DE number 5695268
scientific article