Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
||
Line 2: | Line 2: | ||
denotes the multiplication operation, the structure (S, *) forms | denotes the multiplication operation, the structure (S, *) forms | ||
− | + | '''(A) A Group''' | |
(B) A Ring | (B) A Ring |
Consider the set S = $\{1, ω, ω^2\}$, where $ω$ and $ω^2$ 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
We can directly answer this question as "A Group", because other three options require two operations over structure, but let us see whether (S, *) satisfies group properties or not.
Thus, S satisfies all 4 properties of group, so it is a group. In fact, S is an abelian group, because it also satisfies commutative
property.
So, option (A) is correct.
Consider the set S = $\{1, ω, ω^2\}$, where $ω$ and $ω^2$ 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
We can directly answer this question as "A Group", because other three options require two operations over structure, but let us see whether (S, *) satisfies group properties or not.
Thus, S satisfies all 4 properties of group, so it is a group. In fact, S is an abelian group, because it also satisfies commutative
property.
So, option (A) is correct.