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Unit-III : Algebraic Structures

Unit-III : Algebraic Structures Algebraic Structures : Algebraic Systems: Examples and General Properties, Semi groups and Monoids, Polish expressions and their compilation, Groups: Definitions and Examples, Subgroups and Homomorphism s, Group Codes. Lattices and Boolean algebra: Lattices and Partially Ordered sets, Boolean algebra. Algebraic systems N = { , , , ,.. } = Set of all natural numbers. Z = { 0, , , , , .. } = Set of all integers. Q = Set of all rational numbers. R = Set of all real numbers. Binary Operation: The binary operator * is said to be a binary operation (closed operation) on a non- empty set A, if a * b A for all a, b A (Closure property).

Unit-III : Algebraic Structures Algebraic Structures: Algebraic Systems: Examples and General Properties, Semi groups and Monoids, Polish expressi ons and their compilation, Groups: Definitions and Examples, Subgroups and Homomorphism [s, Group Codes. Lattices and Boolean algebra: Lattices and Partially Ordered sets, Boolean algebra.

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