A.) define the following : ring and domain B.) give an example of a ring that is

Question

A.) define the following : ring and domain
B.) give an example of a ring that is a domain and an example of a ring that is not a domain , explaining the distinguishing characteristics of each example . A.) define the following : ring and domain
B.) give an example of a ring that is a domain and an example of a ring that is not a domain , explaining the distinguishing characteristics of each example .
B.) give an example of a ring that is a domain and an example of a ring that is not a domain , explaining the distinguishing characteristics of each example .

Explanation / Answer

Ring: A ring R is an abelian group with a multiplication operation ( a,b)?abwhich is associative, and satisfies the distributive laws

a(b+c) =ab+ac,

(a+b)c=ac+bc

with identity element 1.

Intregal Domain: An integral domain is a commutative ring with an identity (1 ? 0) with no zero-divisors.
That is ab = 0 ? a = 0 or b = 0

B. Z is ring and domin, Z4 is ring but not intregal domain as 2.2=0 in Z4, so 2 is a divisor of zero.

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