20. Suppose R is a commutative ring and [R]= 30. If I is an ideal of R and |I| = 10, prove that I is a maximal ideal. %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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17. Let H and K be ideals of a ring R. Show that HNK is an ideal of R.
18. List the elements of the principal ideals in Zg:
<2>; <6>; <3>; <5>.
19. Find all maximal ideals and all prime ideals in
(b)
(a) Z8
Z10
(c)
Z12
20. Suppose R is a commutative ring and R= 30. If I is an ideal of R and |I = 10, prove
that I is a maximal ideal.
Transcribed Image Text:17. Let H and K be ideals of a ring R. Show that HNK is an ideal of R. 18. List the elements of the principal ideals in Zg: <2>; <6>; <3>; <5>. 19. Find all maximal ideals and all prime ideals in (b) (a) Z8 Z10 (c) Z12 20. Suppose R is a commutative ring and R= 30. If I is an ideal of R and |I = 10, prove that I is a maximal ideal.
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