True.

Here's why:

A ring R = nZ consists of all the integers that are multiples of n. A zero-divisor in a ring is a nonzero element a such that there exists another nonzero element b in the ring where the product ab = 0.

If n is not a prime number, it means that n can be expressed as a product of two integers a and b (where a, b 1). In the ring R = nZ, both an and bn are elements. Their product is (an)(bn) = abn = n^2 = 0 (in the ring nZ).

Therefore, if n is not a prime number, the ring R = nZ has nonzero zero-divisors.

Question

True.

Here's why:

A ring R = nZ consists of all the integers that are multiples of n. A zero-divisor in a ring is a nonzero element a such that there exists another nonzero element b in the ring where the product ab = 0.

If n is not a prime number, it means that n can be expressed as a product of two integers a and b (where a, b > 1). In the ring R = nZ, both an and bn are elements. Their product is (an)(bn) = abn = n^2 = 0 (in the ring nZ).

Therefore, if n is not a prime number, the ring R = nZ has nonzero zero-divisors.

Knowee AI · Accepted Answer

True.

Here's why:

A ring R = nZ consists of all the integers that are multiples of n. A zero-divisor in a ring is a nonzero element a such that there exists another nonzero element b in the ring where the product ab = 0.

If n is not a prime number, it means that n can be expressed as a product of two integers a and b (where a, b > 1). In the ring R = nZ, both an and bn are elements. Their product is (an)(bn) = abn = n^2 = 0 (in the ring nZ).

Therefore, if n is not a prime number, the ring R = nZ has nonzero zero-divisors.

The ring 𝑅=𝑛ℤ has nonzero zero-divisors if 𝑛 is not prime. True or false

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