Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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de ve ng er Q1: what's the relation between prime and semiprime ideals. Q2: Define prime and semiprime ideals. Q3: If f and g are polynomials in R[x]. what are deg(f +g) and deg(f.g)? Q4: Define ring. Is every subset of a ring R also a ring? Q5: Define nilpotent element. Are 1 and 3 nilpotent elements of Z,? Q6: Define the Boolean ring. Is (Z,+,.) Boolean? Q7: Define the cancelation law. Is it sațisfy in any ring? Q8: What is the difference between homomorphism and isomorphism? Q9: Define maximal ideal, prime ideal. Q10: Define principal ideal ring/ nil radical. Q11: Explain the relationship/between ideal and subring. Q12: Define the concept of field. Is Z a field? Q13: Define and give an example for (integral domain ring, zero divisor). Q14: Define subring. Is the set S = is a subring of the ring M of all 2 x 2 matrices? Q15: Define the concept of ideal and then show that the set I = {(: ): a, b e R} is not an ideal of the ring of all 2 x 2 matrices. 016: What's mean by a nilpotent element of a ring R? Find all nilpotent elements of Zg. Q17: a. Let R be a ring and I, 12 be ideals of R. Is I, UI, an ideal of R? b. True or False: The set of even integers is a commutative ring. Q18: a. Find the zero-divisors of Z,.
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Transcribed Image Text:de ve ng er Q1: what's the relation between prime and semiprime ideals. Q2: Define prime and semiprime ideals. Q3: If f and g are polynomials in R[x]. what are deg(f +g) and deg(f.g)? Q4: Define ring. Is every subset of a ring R also a ring? Q5: Define nilpotent element. Are 1 and 3 nilpotent elements of Z,? Q6: Define the Boolean ring. Is (Z,+,.) Boolean? Q7: Define the cancelation law. Is it sațisfy in any ring? Q8: What is the difference between homomorphism and isomorphism? Q9: Define maximal ideal, prime ideal. Q10: Define principal ideal ring/ nil radical. Q11: Explain the relationship/between ideal and subring. Q12: Define the concept of field. Is Z a field? Q13: Define and give an example for (integral domain ring, zero divisor). Q14: Define subring. Is the set S = is a subring of the ring M of all 2 x 2 matrices? Q15: Define the concept of ideal and then show that the set I = {(: ): a, b e R} is not an ideal of the ring of all 2 x 2 matrices. 016: What's mean by a nilpotent element of a ring R? Find all nilpotent elements of Zg. Q17: a. Let R be a ring and I, 12 be ideals of R. Is I, UI, an ideal of R? b. True or False: The set of even integers is a commutative ring. Q18: a. Find the zero-divisors of Z,.
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