Sheffer stroke R$_{0}-$algebras

Document Type : Research Paper


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.


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.


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