GATE | GATE CS 2010 | Question 4

Consider the set S = {1, ω, ω2}, where ω and w² are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms
(A) A group
(B) A ring
(C) An integral domain
(D) A field


Answer: (A)

Explanation: A group is a set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms, namely closure, associativity, identity and invertibility. (Source: http://en.wikipedia.org/wiki/Group_(mathematics)

(S, *)  is a group with identity as 1

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