Question
Give an example, with justification, of each of the following:
i) a zero divisor in Z5 ,
ii) an element of C[0, 1] which is not a zero divisor,
iii) a subring of an integral domain which is not an integral domain.
Answer :
Word Count : 257
_______ ___ __________ __________ _____.
______ _______ _____ _____ ________ _______ ______ ___.
______ __________ ______ ___ ____ _____ ________.
_______ ___ ________ ________ ______ _________ ________ _________ ____ ____ _______.
_______ ____ ___ ______ ______ ________.
______ ____ ________ _____ ___.
____ ________ _______ ___ _____ ______ __________ _____ ________.
__________ _________ _____ _____ ____ _____ _____ _________ __________.
_____ ____ _________ __________ _____ ________ ____ __________ ________ ____.
_________ _____ _____ ________ _________.
____ __________ ______ _______ _______ ________.
________ _________ ___ ____ ___ _____ _________ __________ ______ ________ __________ ________.
__________ ______ ________ _________ _______.
_________ _______ _________ ______ _________ ________ ______ __________ ________ ___.
____ ________ __________ ___ _________ ______ ______ ______ ______ ____.
______ _____ __________ _______ ___ _____ __________ _____ _________ __________ ___.
___ _______ ___ _____ _____.
______ ______ _______ __________ _______ _______ __________ ______ _________ ________ ________.
________ ____ ______ ___ ______ ____ _______ _____ _____ ______ _______ _______.
________ _______ ______ ___ ____ __________ __________ _____ ______ ______ _________ _______.
_________ __________ ______ _________ ______ __________ __________ _______ ______.
_______ ____ __________ ____ _______.
_______ ____ _________ ____ ___ ________ ________.
Skip in 10
i) In Z5 (the ring of integers modulo 5), the element 0 is a zero divisor. This is because, if you multiply 0 by any non-zero element, such as 1, 2, 3, or 4, you get 0 as the result, which is not equal to the multiplicative identity 1. Thus, 0 * a = 0 for some non-zero 'a' in Z5, making 0 a zero divisor.
ii)
______ _______ _____ _____ ________ _______ ______ ___.
______ __________ ______ ___ ____ _____ ________.
_______ ___ ________ ________ ______ _________ ________ _________ ____ ____ _______.
_______ ____ ___ ______ ______ ________.
______ ____ ________ _____ ___.
____ ________ _______ ___ _____ ______ __________ _____ ________.
__________ _________ _____ _____ ____ _____ _____ _________ __________.
_____ ____ _________ __________ _____ ________ ____ __________ ________ ____.
_________ _____ _____ ________ _________.
____ __________ ______ _______ _______ ________.
________ _________ ___ ____ ___ _____ _________ __________ ______ ________ __________ ________.
__________ ______ ________ _________ _______.
_________ _______ _________ ______ _________ ________ ______ __________ ________ ___.
____ ________ __________ ___ _________ ______ ______ ______ ______ ____.
______ _____ __________ _______ ___ _____ __________ _____ _________ __________ ___.
___ _______ ___ _____ _____.
______ ______ _______ __________ _______ _______ __________ ______ _________ ________ ________.
________ ____ ______ ___ ______ ____ _______ _____ _____ ______ _______ _______.
________ _______ ______ ___ ____ __________ __________ _____ ______ ______ _________ _______.
_________ __________ ______ _________ ______ __________ __________ _______ ______.
_______ ____ __________ ____ _______.
_______ ____ _________ ____ ___ ________ ________.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.