ABSTRACT
This chapter discusses some algebraic properties of lattices and the basic concepts related to semi groups and monoids. The set of algebraic systems with one binary operation on the set, have useful applications in several fields like the theory of finite state machines, coding theory and sequential machines. The chapter also discusses Lattices with universal lower and universal upper bounds. An element in an algebraic system is said to be an identity if it is both a left identity and a right identity. The chapter considers some algebraic systems with one binary operation on the set. These systems have useful applications in the theory of finite state machines, coding theory, and sequential mechanics.
