The concept of S-algebra and its properties

Abstract

In this paper, a new type of algebra namely S-algebra is introduced. The partial ordering on S-algebra is introduced, some examples of S-algebras are given and some equivalent conditions for an S-algebra to become a distributive lattice are given by introducing a partial order S-algebra x≤y, if y∧x=x. This partial ordering leads to some S-algebras. Congruences on S-algebra are introduced and some properties on congruences are proved. The concept of central element in an S-algebra is introduced. By using a central element a of S, S-algebra can be decomposed into two S-algebras and some important properties are emphasized.