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In the semigroup with identity (R,) we define Va E R+, fa: (R, +) → (R, +) by Vx € R, fa (x) = ax. Let us now consider T = {fa: R⇒ R/ a € R*} and (t,0). So, a. Va E R* is fa E T a morphism? b. Va E R* is fa E Ta monomorphism? c. Va E R* is fa E Ta epimorphism? d. Va E R* is fa Et invertible? e. For va € R+, determine Ker fa

In the semigroup with identity (R,) we define Va E R+, fa: (R, +) → (R, +) by Vx € R, fa (x) = ax. Let us now consider T = {fa: R⇒ R/ a € R*} and (t,0). So, a. Va E R* is fa E T a morphism? b. Va E R* is fa E Ta monomorphism? c. Va E R* is fa E Ta epimorphism? d. Va E R* is fa Et invertible? e. For va € R+, determine Ker fa

Advanced Engineering Mathematics
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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In the semigroup with identity (IR ,;) we define Va E R†, fa: (R, +) → (IR, +) by Vx € R, fa (x) = ax. Let us now consider t = {fa: R → R / a € R*} and (t,0). So, a. Va e Rt is fa Eta morphism? b. Va e R* is fa Eta monomorphism? c. Va E R* is fa E ta epimorphism? d. Va E Rt is fa Et invertible? e. For Va E R*, determine Ker fa
Transcribed Image Text:In the semigroup with identity (IR ,;) we define Va E R†, fa: (R, +) → (IR, +) by Vx € R, fa (x) = ax. Let us now consider t = {fa: R → R / a € R*} and (t,0). So, a. Va e Rt is fa Eta morphism? b. Va e R* is fa Eta monomorphism? c. Va E R* is fa E ta epimorphism? d. Va E Rt is fa Et invertible? e. For Va E R*, determine Ker fa
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