ELEMENTS OF MODERN ALGEBRA8th EditionGilbert Publisher: CENGAGE LISBN: 9780357671139
ELEMENTS OF MODERN ALGEBRA
Solutions for ELEMENTS OF MODERN ALGEBRA
Problem 1TFE:
True or False
Label each of the following statements as either true or false where represents a...Problem 4E:
Consider the following polynomial over Z9, where a is written for [ a ] in Z9: f(x)=2x3+7x+4,...Problem 5E:
5. Decide whether each of the following subset is a subring of , and justify your decision in each...Problem 6E:
Determine which subset in Exercise 5 are ideals of R[x] and which are principal ideals. Justify your...Problem 7E:
Prove that [ x ]={ a0+a1x+...+anxna0=2kfork }, the set of all polynomials in [ x ] with even...Problem 10E:
Let R be a commutative ring with unity. Prove that deg(f(x)g(x))degf(x)+degg(x) for all nonzero...Problem 11E:
11. a. List all the polynomials in that have degree 2.
b. Determine which of the polynomials in...Problem 12E:
a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant...Problem 14E:
14. Prove or disprove that is a field if is a field.
Problem 16E:
a. If R is a commutative ring with unity, show that the characteristic of R[ x ] is the same as the...Problem 18E:
18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is...Problem 20E:
Consider the mapping :Z[ x ]Zk[ x ] defined by (a0+a1x++anxn)=[ a0 ]+[ a1 ]x++[ an ]xn, where [ ai ]...Problem 21E:
Describe the kernel of epimorphism in Exercise 20. Consider the mapping :Z[ x ]Zk[ x ] defined by...Problem 22E:
Assume that each of R and S is a commutative ring with unity and that :RS is an epimorphism from R...Browse All Chapters of This Textbook
Chapter 1.1 - SetsChapter 1.2 - MappingsChapter 1.3 - Properties Of Composite Mappings (optional)Chapter 1.4 - Binary OperationsChapter 1.5 - Permutations And InversesChapter 1.6 - MatricesChapter 1.7 - RelationsChapter 2.1 - Postulates For The Integers (optional)Chapter 2.2 - Mathematical InductionChapter 2.3 - Divisibility
Chapter 2.4 - Prime Factors And Greatest Common DivisorChapter 2.5 - Congruence Of IntegersChapter 2.6 - Congruence ClassesChapter 2.7 - Introduction To Coding Theory (optional)Chapter 2.8 - Introduction To Cryptography (optional)Chapter 3.1 - Definition Of A GroupChapter 3.2 - Properties Of Group ElementsChapter 3.3 - SubgroupsChapter 3.4 - Cyclic GroupsChapter 3.5 - IsomorphismsChapter 3.6 - HomomorphismsChapter 4.1 - Finite Permutation GroupsChapter 4.2 - Cayley’s TheoremChapter 4.3 - Permutation Groups In Science And Art (optional)Chapter 4.4 - Cosets Of A SubgroupChapter 4.5 - Normal SubgroupsChapter 4.6 - Quotient GroupsChapter 4.7 - Direct Sums (optional)Chapter 4.8 - Some Results On Finite Abelian Groups (optional)Chapter 5.1 - Definition Of A RingChapter 5.2 - Integral Domains And FieldsChapter 5.3 - The Field Of Quotients Of An Integral DomainChapter 5.4 - Ordered Integral DomainsChapter 6.1 - Ideals And Quotient RingsChapter 6.2 - Ring HomomorphismsChapter 6.3 - The Characteristic Of A RingChapter 6.4 - Maximal Ideals (optional)Chapter 7.1 - The Field Of Real NumbersChapter 7.2 - Complex Numbers And QuaternionsChapter 7.3 - De Moivre’s Theorem And Roots Of Complex NumbersChapter 8.1 - Polynomials Over A RingChapter 8.2 - Divisibility And Greatest Common DivisorChapter 8.3 - Factorization In F [x]Chapter 8.4 - Zeros Of A PolynomialChapter 8.5 - Solution Of Cubic And Quartic Equations By Formulas (optional)Chapter 8.6 - Algebraic Extensions Of A Field
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More Editions of This Book
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EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 9780100475755
Elements Of Modern Algebra
8th Edition
ISBN: 9781285463230
EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 8220100475757
Elements Of Modern Algebra
8th Edition
ISBN: 9781285965918
Elements of Modern Algebra
5th Edition
ISBN: 9780534373511
Elements of Modern Algebra
6th Edition
ISBN: 9780534402648
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