2 votes 2 votes does it satisfy for every subset of R? Engineering Mathematics group-theory discrete-mathematics set-theory&algebra abelian-group engineering-mathematics + – raviyogi asked Jan 24, 2018 raviyogi 496 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes every element in S will have unique identity and inverse, for identity, e=0 x*0=x { x+0+0*x = x } for inverse, let y be inverse of x x*y=0 x+y+xy=0 y=-x/(1+x) { 1+x !=0) x!= -1 Learner_jai answered Jan 14, 2019 Learner_jai comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Yes, S is the subgroup closed under * and it does show the abelian property. Remember its mentioned that s is improper subset of R, thus it should satisfy the property for the most. rish1602 answered Jun 22, 2021 rish1602 comment Share Follow See all 0 reply Please log in or register to add a comment.