et R = {[ la, b e z}and let o:R – Z be defined by : 0( = a 1) o is a ring a) Homomorphism. b) Isomorphism c) None 2) ker (o) is generated by a) 3) R/ker (4) = a) z b) Q c) R d) None 4) Ker (4) is: а) Prime ideal not maximal b) Maximal ideal not prime c) Both maximal and prime d) None

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.4: Maximal Ideals (optional)
Problem 8E
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I want all parts please to get sure of my urgent homework
Let R = { la. b e Z}and let p:R – Z be defined by : 0( ) =
%3D
-
1) o is a ring
a)
Homomorphism.
b)
Isomorphism
c)
None
2) ker (4) is generated by
a)
b) : )
c)
3) R/ker (4) =
a) z
b) Q
c)
R
d) None
4) Ker (4) is:
a)
Prime ideal not maximal
b)
Maximal ideal not prime
c) Both maximal and prime
d) None
Transcribed Image Text:Let R = { la. b e Z}and let p:R – Z be defined by : 0( ) = %3D - 1) o is a ring a) Homomorphism. b) Isomorphism c) None 2) ker (4) is generated by a) b) : ) c) 3) R/ker (4) = a) z b) Q c) R d) None 4) Ker (4) is: a) Prime ideal not maximal b) Maximal ideal not prime c) Both maximal and prime d) None
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