9th Edition

ISBN: 9781305657960

Author: Joseph Gallian

Publisher: Cengage Learning

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Chapter 12, Problem 39E

Suppose that R is a ring with unity 1 and a is an element of R suchthat a 2 = 1 . Let S = { a r a | r ∈ R } . Prove that S is a subring of R.Does S contain 1?

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Chapter 12, Problem 38E

Chapter 12, Problem 40E

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Chapter 12 Solutions

Contemporary Abstract Algebra

Ch. 12 - The ring {0, 2, 4, 6, 8} under addition and...Ch. 12 - Find an integer n that shows that the rings Zn...Ch. 12 - Show that a ring is commutative if it has the...Ch. 12 - Prove that the intersection of any collection of...Ch. 12 - Let a, b, and c be elements of a commutative ring,...Ch. 12 - Let a andb belong to a ring R and let mbe an...Ch. 12 - Show that if m and n are integers and a and b are...Ch. 12 - Show that a ring that is cyclic under addition is...Ch. 12 - Let R be a ring. The center of R is the set...Ch. 12 - Let R be a commutative ring with unity and let...

Ch. 12 - Show that a unit of a ring divides every element...Ch. 12 - Suppose that R is a ring with unity 1 and a is an...Ch. 12 - Suppose that there is a positive even integer n...Ch. 12 - Prob. 45E Ch. 12 - Show that 2Z3Z is not a subring of Z.

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Suppose that R is a ring with unity 1 and a is an element of R suchthat a 2 = 1 . Let S = { a r a | r ∈ R } . Prove that S is a subring of R .Does S contain 1?

Solution Summary: The author explains that S is a subring of R, and that it contains 1.

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Chapter 12 Solutions