Sheffer stroke R$_{0}-$algebras
نویسندگان
1 Department of Mathematics, Faculty of Arts and Sciences, Izmir University of Economics, Balcova, Izmir, Turkiye.
2 Department of Mathematics, Faculty of Science, Ege University, Bornova, Izmir, Turkiye.
3 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
doi
10.22034/as.2023.3006چکیده
The main objective of this study is to introduce Sheffer stroke R$_{0}-$algebra (for short, SR$_{0}-$ algebra). Then it is stated that the axiom system of a Sheffer stroke R$_{0}-$algebra is independent. It is indicated that every Sheffer stroke R$_{0}-$algebra is R$_{0}-$algebra but specific conditions are necessarily for the inverse. Afterward, various ideals of a Sheffer stroke R$_{0}-$algebra are defined, a congruence relation on a Sheffer stroke R$_{0}-$algebra is determined by the ideal and quotient Sheffer stroke R$_{0}-$algebra is built via this congruence relation. It is proved that quotient Sheffer stroke R$_{0}-$algebra constructed by a prime ideal of this algebra is totally ordered and the cardinality is less than or equals to 2. After all, important conclusions are obtained for totally ordered Sheffer stroke R$_{0}-$algebras by applying various properties of prime ideals.
