Suppose that ≺D,+,⋅≻ is a well-ordered integral domain. Then the least positive element in D is the unity e∈D, since if a∈Dp such that e>a, then e−a∈Dp⟹a(e−a)∈Dp⟹a−a2∈Dp. I.
Suppose that ≺D,+,⋅≻ is a well-ordered integral domain. Then the least positive element in D is the unity e∈D, since if a∈Dp such that e>a, then e−a∈Dp⟹a(e−a)∈Dp⟹a−a2∈Dp. I.
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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Suppose that ≺D,+,⋅≻ is a well-ordered
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Step 1: Step 1
Suppose that ≺D,+,⋅≻ is a well-ordered integral domain and let e be the least positive element in D.
If there exists an element a∈
But
so we have
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