Let R be a commutative ring with identity and let ,g e R[[xJJ. Denote by In ,
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Let R be a commutative ring with identity and let ∫,g e R[[xJJ. Denote by In ∫, the "' initial degree of ∫ (that is, the smallest n such that an ≠ 0, where Show that
(a) In (∫ + g) ≥ min (In ∫, In g).
(b) In (∫g) ≥ In ∫ + In g.
(c) If R is an integral domain, In (∫g) = In ∫ + In g.
Transcribed Image Text:
f= Σ dixi). i=0
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To prove these statements we will use properties of power series and their coefficients Lets go through each part step by step a In g min In In g Lets ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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