Katıcan TuğçeÖner, T.Saeid, A.B.2023-09-112023-09-1120232423-3447https://doi.org/10.22034/as.2023.3006https://hdl.handle.net/20.500.14365/4818The main objective of this study is to introduce Sheffer stroke R0−algebra (for short, SR0− algebra). Then it is stated that the axiom system of a Sheffer stroke R0−algebra is independent. It is indicated that every Sheffer stroke R0−algebra is R0−algebra but specific conditions are necessarily for the inverse. Afterward, various ideals of a Sheffer stroke R0−algebra are defined, a congruence relation on a Sheffer stroke R0−algebra is determined by the ideal and quotient Sheffer stroke R0−algebra is built via this congruence relation. It is proved that quotient Sheffer stroke R0−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 R0−algebras by applying various properties of prime ideals. © 2023 Yazd University.eninfo:eu-repo/semantics/closedAccess(prime) Ideal(Sheffer stroke) R0−algebraCongruence relationSheffer strokeArticle10.22034/as.2023.30062-s2.0-85164465241