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man result with the lonowing important observation. Remark 5. If I is a two-sided ideal of LK (E) and μ = ₁+ +n is in I, where 1,...,n are monomials in LK (E), then i = s(i)ur (i) is the sum of those uj whose sources are all the same and whose ranges are all the same; specifically, the sum of those μ, for which s(u) = s(μ₁) and r(uj) = r(ui). Moreover, Yi E I. Thus we may write u = ₁ + + Ym, with each Yi with the above properties.

man result with the lonowing important observation. Remark 5. If I is a two-sided ideal of LK (E) and μ = ₁+ +n is in I, where 1,...,n are monomials in LK (E), then i = s(i)ur (i) is the sum of those uj whose sources are all the same and whose ranges are all the same; specifically, the sum of those μ, for which s(u) = s(μ₁) and r(uj) = r(ui). Moreover, Yi E I. Thus we may write u = ₁ + + Ym, with each Yi with the above properties.

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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man result with the lonowing important Observation. Remark 5. If I is a two-sided ideal of LK (E) and μ = μ₁+ +n is in I, where 1,...,n are monomials in LK (E), then i = s(i)ur(i) is the sum of those uj whose sources are all the same and whose ranges are all the same; specifically, the sum of those μ, for which s(u) = s(μ₁) and r(u) = r(ui). Moreover, Yi E I. Thus we may write u = ₁ + + Ym, with each Yi with the above properties.
Transcribed Image Text:man result with the lonowing important Observation. Remark 5. If I is a two-sided ideal of LK (E) and μ = μ₁+ +n is in I, where 1,...,n are monomials in LK (E), then i = s(i)ur(i) is the sum of those uj whose sources are all the same and whose ranges are all the same; specifically, the sum of those μ, for which s(u) = s(μ₁) and r(u) = r(ui). Moreover, Yi E I. Thus we may write u = ₁ + + Ym, with each Yi with the above properties.
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