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Let A = (a1, . . as) and B = defines the product of the ideals to be (B1,.. Bt) be ideals in K. The text AB := (a1ß1, . .., a;ßj,.….. , asßt). Prove that the product of ideals A and B defined by n AB := {> a;b; : a; E A, b; E B,n E Z+} i=1 is equivalent to the definition of AB in the text.

Let A = (a1, . . as) and B = defines the product of the ideals to be (B1,.. Bt) be ideals in K. The text AB := (a1ß1, . .., a;ßj,.….. , asßt). Prove that the product of ideals A and B defined by n AB := {> a;b; : a; E A, b; E B,n E Z+} i=1 is equivalent to the definition of AB in the text.

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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Let A = (a1,..., a,) and B = (81,..., B) be ideals in K. The text defines the product of the ideals to be AB := (a1ß1, ..., a;Bj, ..., asBt). Prove that the product of ideals A and B defined by n AB := {> a;b; : a; E A, b; E B, n E Z†} i=1 is equivalent to the definition of AB in the text.
Transcribed Image Text:Let A = (a1,..., a,) and B = (81,..., B) be ideals in K. The text defines the product of the ideals to be AB := (a1ß1, ..., a;Bj, ..., asBt). Prove that the product of ideals A and B defined by n AB := {> a;b; : a; E A, b; E B, n E Z†} i=1 is equivalent to the definition of AB in the text.
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