For any positive integer m, show that every subgroup of Zm is an ideal of Zm-

Q: Let I be an ideals of a ring R and S C R: (i) Show that InS is an ideal of S. Is it also an ideal of…

A: I is an ideal of a ring R and S is subring of R. So if x∈I∩S ⇒x∈I and x∈S sx∈I     for some s∈S and…

Q: Find all ideals of Z3 [i] . Show your work. (-

A: ℤ3i is clearly a field  because ℤpi is a field if p≡3 (mod 4). Thus 3≡3(mod 4) therefore ℤ3i is a…

Q: Show that A is ideal of A+B? IS an

A: According to questionWe have to show that A is an ideal of A+B

Q: Give an example of a commutative ring R with unity and a maximalideal I of R such that I[x] is not a…

A: In this question,  we have to give an example of a commutative ring R with unity and a maximal ideal…

Q: Q6:Let (R,+..) and (R.+.) be commutative rings with identities. Given f is a homomorphism from (R,…

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Q: Show that a commutative ring R with unity is a field if and only if its only two ideals are (0) and…

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Q: Show that the ideal I = (6) is a maximal ideal of E.

A: Show that the ideal I = (6) is a maximal ideal of E.