5
Algebraic Structures
The algebraic structures like semigroup, monoid, group, ring and field have wide applications in many disciplines and in particular to binary coding.
5.1 BINARY OPERATIONS
Definition 5.1
A collection of objects with operations defined on them and the accompanying properties form a Mathematical Structure or System.
For example, the collection of sets with the operations of union, intersection, and complement and their accompanying properties is a discrete mathematical structure. We denote this structure by [sets, ∪, ∩, −].
Similarly, the collection of 3 × 3 matrices with the operations of addition, multiplication and transpose and their accompanying properties is a mathematical structure. We denote this structure by [3 ...
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