Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101Relation between Sheffer Stroke and Hilbert algebras2452688751010.29252/cgasa.14.1.245ENTahsinOnerDepartment of Mathematics, Ege University, 35100 Izmir, Turkey0000-0002-6514-4027TugceKaticanDepartment of Mathematics, Ege University, 35100 Izmir, TurkeyArshamBorumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of
Kerman, Kerman, Iran.Journal Article20200607In 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.https://cgasa.sbu.ac.ir/article_87510_0c7d162f32c37f1f0916408dfd6b27ae.pdf