Relation between Sheffer Stroke and Hilbert algebras
Articles > Article · 2021
Authors: Tahsin ÖNER, Tugce Katican, Arsham Borumand Saeid
Categories and General Algebraic Structures with Application, Journal Indexed in SCI Expanded, International, Scopus, 2021, vol 14, pp 245-268
Summary
In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of Sheffer stroke and a Hilbert algebra. After it is shown that the axioms of Sheffer stroke Hilbert algebra are independent, it is given some properties of this algebraic structure. Then it is stated the relationship between Sheffer stroke Hilbert algebra and Hilbert algebra by defining a unary operation on Sheffer stroke Hilbert algebra. Also, it is presented deductive system and ideal of this algebraic structure. It is defined an ideal generated by a subset of a Sheffer stroke Hilbert algebra, and it is constructed a new ideal of this algebra by adding an element of this algebra to its ideal.