Let S be a prime ideal of R and suppose that a product a₁a₂a3... an, of elements of R, belongs to S. Then at least one of a₁, i = 1,2,3,..., n, belongs to S.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let \( S \) be a prime ideal of \( R \) and suppose that a product \( a_1a_2a_3 \ldots a_n \), of elements of \( R \), belongs to \( S \). Then at least one of \( a_i \), \( i = 1, 2, 3, \ldots, n \), belongs to \( S \).
Transcribed Image Text:Let \( S \) be a prime ideal of \( R \) and suppose that a product \( a_1a_2a_3 \ldots a_n \), of elements of \( R \), belongs to \( S \). Then at least one of \( a_i \), \( i = 1, 2, 3, \ldots, n \), belongs to \( S \).
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Let S be a prime ideal of R and suppose that a product space a subscript 1 a subscript 2 a subscript 3... a subscript n, of elements of R, belongs to S. Then prove that at least one of ai , i=1,2,3,...,n, belongs to S.

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