A view on state operators in Sheffer stroke basic algebras

In this paper, we present constructions of Riecan, Bosbach and internal and general states on Sheffer stroke basic algebra A. We deal with some characteristic features and independency of axiomatic system of forementioned states. We prove that a Riecan state corresponds to a Bosbach state or vice versa. In the sequel, we introduce faithful and fixed set generated by internal states on A. We demonstrate that each Sheffer stroke basic algebra is also a Sheffer stroke basic algebra under internal state. In addition, we mention about internal state-(filter, compatible filter and prime filter) on A and their related results. We touch on internal state congruence and investigate its relation with filters. We are interested in finding whether general states have implied Riecan and Bosbach states or not. We handle the notion of general state-morphism and some related results on A. In order to support mentioned concepts, we give place to some attractive examples.