3 votes 3 votes Consider the set $S=\{1,\omega,\omega ^2\}$, where $\omega$ and $\omega^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S,*)$ forms: A group A ring An integral domain A field Set Theory & Algebra nielit2016dec-scientistb-it discrete-mathematics set-theory&algebra group-theory + – admin asked Mar 31, 2020 retagged Oct 23, 2020 by Krithiga2101 admin 693 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes $*$ $1$ $w$ $w^{2}$ $1$ $1$ $w$ $w^{2}$ $w$ $w$ $w^{2}$ $1$ $w^{2}$ $w^{2}$ $1$ $w$ A Group is an algebraic structure which satisfies 1) closure 2) Associativity 3) Have Identity element 4) Invertible Over '*' operation the $ S$ = {$1$, $w$, $w^{2}$ } satisfies the above properties. The identity element is $1$ and inverse of $1$ is$ 1$, inverse of$ w$ is $w^{2}$ and inverse of$ w^{2}$ is $w$ https://gateoverflow.in/1150/gate2010-4 https://www.geeksforgeeks.org/gate-gate-cs-2010-question-4/ Mohit Kumar 6 answered May 27, 2020 Mohit Kumar 6 comment Share Follow See all 2 Comments See all 2 2 Comments reply DAWID15 commented Dec 13, 2021 reply Follow Share Does it follow commutative property? 0 votes 0 votes s_dr_13 commented Jan 19, 2022 reply Follow Share What is the meaning of ring here ? 0 votes 0 votes Please log in or register to add a comment.