{; la, b e R} and let o:S → R be defined by : 0(; ) =eLet S =1) ois a ringa)Homomorphism.b)Isomorphismc)None2) ker (4) is generated byro 1]TO 01b) :ro 013) S/ker (4) =a) zb) Qc)Rd) None4) Ker (4) is:a)Prime ideal not maximalb) Maximal ideal not primec)Both maximal and primed) None

Using conditions of homomorphism of rings and isomorphism theorem we can answer this questions

{E Jla, b e R} and let :S –R be defined by : 0( ) = 1) ois a ring a) Homomorphism. b) Isomorphism c) None 2) ker (4) is generated by ro 1] a) 6 b) G ) TO 01 ro 01 3) S/ker (4) = a) Z b) Q c) R d) None

{E Jla, b e R} and let :S –R be defined by : 0( ) = 1) ois a ring a) Homomorphism. b) Isomorphism c) None 2) ker (4) is generated by ro 1] a) 6 b) G ) TO 01 ro 01 3) S/ker (4) = a) Z b) Q c) R d) None

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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Question

{; la, b e R} and let o:S → R be defined by : 0(; ) =e
Let S =
1) ois a ring
a)
Homomorphism.
b)
Isomorphism
c)
None
2) ker (4) is generated by
ro 1]
TO 01
b) :
ro 01
3) S/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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