Algebraic Structures of Complete Residue Systems 

In the following section we will introduce complete residue systems, i.e. sets of integers which represent all possible congruence classes modulo a positive integer $m > 0.$ We will also study their algebraic structure for prime and composite modules $m.$

| | | | created: 2019-04-19 06:41:31 | modified: 2019-06-22 08:34:02 | by: bookofproofs | references: [1272], [8152]

1.Definition: Complete Residue System 

2.Proposition: Addition, Subtraction and Multiplication of Congruences, the Commutative Ring $\mathbb Z_m$ 

3.Proposition: Cancellation of Congruences With Factor Co-Prime To Module, Field $\mathbb Z_p$ 

4.Proposition: Cancellation of Congruences with General Factor 

5.Proposition: Creation of Complete Residue Systems From Others