Question

Let R and S be rings and
ϕ:R→S
be an isomorphism, the
ϕ
is __________________
monomorphism
endomorphism
Automorphism
homomorphism

Answer 1

homo for sure

Answer 2

An example of an endomorphic map is ___________________
ϕ:Z→Q
ϕ:R→C
ϕ:Z→Z
ϕ:C→R

Answer 3

i think c @Loser66

Answer 4

yup

Answer 5

Let R be the ring[0,1]of all conditions real valued function on the close interval [0,1] and
ϕ:R→R
defined by
ϕ(f)=(1/2)f
then
ϕ
is _______
homomorphism
Endomorphism
Isomorphism
Epimorphism

Answer 6

@Loser66 are you sure or you think?

Answer 7

now, i am sure, since before you typed 12 f, it is nonsense

Answer 8

now it is 1/2 f, makes more sense

Answer 9

have a lot more please help

Answer 10

If G is agroup and H is a subgroup of G.then
the order of G divides the order H
the order of H divides the order G
H1∩G2
has same order as H
H1∩G2
has same order as G

Answer 11

@Loser66

Answer 12

the order of H divides the order of G

Answer 13

I don't know what is H1 or G2

Answer 14

ok.

Answer 15

Consider the subset I={ 0,3,6} of the ring
equivalent of [0] is ------------------
[8,10,12,14,...]
[...,-18,-9,0,9,18,...]
[...,30,36,42,48,54,..]
[...,2,4,6,8,10,...]

Answer 16

@Loser66

Answer 17

What is the ring?

Answer 18

z9

Answer 19

set of multiple of 9

Answer 20

You should understand what is going on

Answer 21

in \(\mathbb Z_9\) the congruence [0] is set of number divided by 9

Answer 22

for example 9 |9 =1 Remainder 0 , this remainder is what it is indicate to congruence 0

Answer 23

9|18 =2 Remainder 0, hence 18 is in the set you are looking for

Answer 24

Suppose I give you 20, then 9|20 = 2 Remainder 2, hence 20 is NOT in the set of congruence 0

Answer 25

Among the options, only {....., -18,-9,0,9,18.......} all terms are multiple of 9. Each term divided by 9 get 0 in remainder. Hence this set is the answer.
Got me?

Answer 26

yes sir

Answer 27

Let
ϕ:R→R′
be a homomorphism of a ring R into a ring R'. The one of these is not true
ϕ(0)=0′
ϕ(−a)=−ϕ(a)
ϕ(e)=e′
ϕ′(s′)
is not a subring of R where S' is a subring

Answer 28

@Loser66

Answer 29

what is \(\phi '\)

Answer 30

im back in 30 minutes

Answer 31

ok sir. will be waiting

Answer 32

thanks

Answer 33

you there?

Answer 34

yes

Answer 35

ok are you back?

Answer 36

but I don't know what is phi ' from the last one, is it inverse of phi?

Answer 37

dont know . dats just the question

Answer 38

i think it is inverse

Answer 39

Actually, among them, the last one seems not true since the homomorphism doesn't give us that homomorphism is onto (surjective) , hence nothing guarantee that S' has pre-image in R

Answer 40

ok

Answer 41

Moreover, all the other choices are correct

Answer 42

ok

Answer 43

Let R be the ring[0,1]of all conditions real valued function on the close interval [0,1] and
ϕ:R→R
defined by
ϕ(f)=1/2f
what is Kerφ

Answer 44

0

Answer 45

let f is in kernel, then \(\phi (f) = 1/2 f =0\) if and only if f =0, Hence f =0 is kernel phi

Answer 46

Let G be a group and
H1
,
H2
normal subgroups of .one of these is a normal subgroup of G
H1∩H2
H1∪H2
H1−H2
A×B

Answer 47

@Loser66