Question

The integer modulo n
A. is not an integral domain if n is prime
B. is always an integral domain
C. forms a ring for any natural number n
D. forms a ring if n is prime​

Answer 1

Answer:

D .froms a ring if n is prime

Answer 2

Answer:

D. forms a ring if n is prime​.

Step-by-step explanation:

• An integer modulus is defined as the when the integer is a division and modulus, it dividend will be the divisor which will convert it into integer quotient and reminder.

• The modulo operator of integer:

Let us consider two prime numbers a and b,

A modulo be n

When we prove this, we get,

The remainder of Euclidean division of a along with n.

Here, a is dividend

N is the divisor.

• To prove:

The integer modulo n forms a ring.

A ring R is called an abelian group with a multiplication operation

(a, b) --> ab

Which  will be the associate.

It will satisfy the rule of distributive laws:

a(b+c) = ab+ac & (a+b)c = ab+ac for a,b, c ∈ r.

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