Question

Find the characteristics of the following

𝑖)2𝑍

𝑖𝑖) 𝑍3 × 𝑍3

𝑖𝑖𝑖)𝑍6 × 𝑍15

Accepted Answer

i:  By , ,the , ,definition , ,if , , forall x , ,nx=0 holds , ,only , ,for , ,n=0, the , ,characteristic , ,is , ,0  In , ,our , ,case , , forall x , ,nx=0 Rightarrow n cdot 2=0 Rightarrow n=0,  thus , ,the , ,characteristic , ,is , ,0  ii:  This , ,ring , ,contains , ,multiplicative , ,identity , , left( 1,1  right)   n left( 1,1  right) =0 Rightarrow  left( n,n  right) =0 Rightarrow 3|n  Minimum , ,positive , ,n , ,is , ,3 Rightarrow The , ,characteristic , ,is , ,3  iii:  This , ,ring , ,contains , ,multiplicative , ,identity , , left( 1,1  right)   n left( 1,1  right) =0 Rightarrow  left( n,n  right) =0 Rightarrow 6|n,15|n  Minimum , ,positive , ,n , ,is , ,LCM left( 6,15  right) =30 Rightarrow The , ,characteristic , ,is , ,30

Question #314869

Expert's answer

Answer in progress...