→ N. Assume that p is multiplicative, i.e.Let 1 € R be an Euclidean domain with the strictly positive Euclidean norm o : R \ {0}P(ab) = p(a)p(b).Show that if a E Ris a unit, then p(a) = 1.(Hint: first show that p(1) = 1)

Given that 1∈R, where R is an Euclidean domain. By given we have φab=φaφb. We prove that if a is an…

Let 1 € R be an Euclidean domain with the strictly positive Euclidean norm p : R \ {0} → N. Assume that p is multiplicative, i.e. p(ab) = p(a)p(b). Show that if a € R is a unit, then ø(a) = 1. (Hint: first show that p(1) = 1)

Let 1 € R be an Euclidean domain with the strictly positive Euclidean norm p : R \ {0} → N. Assume that p is multiplicative, i.e. p(ab) = p(a)p(b). Show that if a € R is a unit, then ø(a) = 1. (Hint: first show that p(1) = 1)

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 mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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→ N. Assume that p is multiplicative, i.e.
Let 1 € R be an Euclidean domain with the strictly positive Euclidean norm o : R \ {0}
P(ab) = p(a)p(b).
Show that if a E Ris a unit, then p(a) = 1.
(Hint: first show that p(1) = 1)

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