If ring (R1, +, *) is isomorphic to ring (R2, +, *) with f being the isomorphism, then prove the following statements: a. f(e1) = e2, where e1 is the identity element for the group (R1, +) and e2 is the identity element of the group (R2, +). b. f(-a) = -f(a), for each element ‘a’ in R1, where –a represent the additive inverse of element ‘a’ in R1 and –f(a) represents the additive inverse of the element f(a) in R2. c. If (R1, +, *) is a ring with (multiplicative) identity I1 and (R2, +, *) is a ring with (multiplicative) identity I2, then f(I1) = I2.

If ring (R1, +, ) is isomorphic to ring (R2, +, ) with f being the isomorphism, then prove the following statements: a. f(e1) = e2, where e1 is the identity element for the group (R1, +) and e2 is the identity element of the group (R2, +). b. f(-a) = -f(a), for each element ‘a’ in R1, where –a represent the additive inverse of element ‘a’ in R1 and –f(a) represents the additive inverse of the element f(a) in R2. c. If (R1, +, ) is a ring with (multiplicative) identity I1 and (R2, +, ) is a ring with (multiplicative) identity I2, then f(I1) = I2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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