Sheffer Stroke BN-algebras and Connected Topics (European Journal of Pure and Applied Mathematics, 2025)
This article introduces the concept of a Sheffer stroke BN-algebra by applying the Sheffer stroke operator | to the BN-algebra axioms and aligning it with the axioms of the Sheffer stroke groupoid. From this definition, properties of Sheffer stroke BN algebras are derived, focusing on the relationship between the axioms and the properties of the special element 0. Furthermore, the notions of Sheffer stroke BN-subalgebras, BN-ideals, and BN-homomorphisms are defined, along with normal subsets of Sheffer stroke BN-algebras, and the relationships between these concepts are explored. It is shown that every normal subset in a Sheffer stroke BN-algebra is a Sheffer stroke BN-subalgebra, but the converse is not necessarily true. This implies that every normal BN-ideal in a Sheffer stroke BN-algebra is also a Sheffer stroke BN-subalgebra. Finally, the properties of the kernel of the Sheffer stroke BN-homomorphism are investigated.
Keywords: BN-algebra, Sheffer stroke, Sheffer stroke BN-algebra, BN-ideal, BN-subalgebra