Congruences of Sheffer stroke basic algebras

Ibrahim Senturk 1 , Tahsin Oner 2 ,  and Arsham Borumand Saeid 3
  • 1 Department of Mathematics, Faculty of Sciences, Ege University, Bornova, 35100, Izmir, Turkey
  • 2 Department of Mathematics, Faculty of Sciences, Ege University, Bornova, 35100, Izmir, Turkey
  • 3 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Iran, Kerman

Abstract

In this paper, congruences and (order, prime and compatible) filters are introduced in Sheffer stroke basic algebras. They are interrelated with each other. Also some relationships between filters and congruences by focusing on their properties in these structures are given. In addition to these, a basic algebra is constructed by the help of compatible filter and 𝒜/ Θ (F). Moreover, a representation theorem for Sheffer stroke basic algebra by using prime filters and 𝒜/ Θ (F) is stated and proved.

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