let
A=M2(Z)
be the ring of
2×2
integral matrices the identity of A,
IA

- anonymous

let
A=M2(Z)
be the ring of
2×2
integral matrices the identity of A,
IA

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- anonymous

@misty1212

- misty1212

is the question asking for the identity matrix?

- anonymous

YES

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## More answers

- misty1212

it is the usual one

- anonymous

HMM. |dw:1434206105315:dw|

- misty1212

\[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\]

- misty1212

yeah that one

- anonymous

OK

- anonymous

Let G be a group and
H1
,
H2
normal subgroups of .one of these is a normal subgroup of G

- misty1212

whew i thought it was going to be some hard ring question, not a nice easy one

- misty1212

you lost me there, was it perhaps a copy and paste fail?

- anonymous

1)H1 INTERCEPT H2
2)H1 UNION H2
3)H1-H2
4)AXB

- misty1212

if \(A_1,H_2\) are normal in \(G\) then \(H_1\cap H_2\) is as well, it is a straightforward check

- misty1212

depending of course on what your definition of a normal subgroup is
there are a couple

- anonymous

OK MA. HAVE SOME MORE...

- misty1212

wait, you don't have to prove it, just pick one?

- anonymous

If R and R'are rings, a mapping
ϕ:R→R′
ring ho morphism if any of these happen
∀a,b,∈R

- anonymous

ϕ(a+b)=ϕ(a)+ϕ(b)
ϕ(a/b)=ϕ(a)−ϕ(b)
ϕ(a.b)=ϕ(a)ϕ(b)
A and C only

- misty1212

wow an abstract algebra class with multiple guess questions?
no proofs just pick?

- anonymous

IM VERY CONFUSE and the book i have does note contain all these.

- misty1212

guess, i bet you get it on the first try
or google ring homorphisms
one hint, no one says division is even DEFINED in a ring

- anonymous

yes. i thought as much. it is multiplication and addition . right?

- misty1212

or just read the top line here
https://en.wikipedia.org/wiki/Ring_homomorphism

- misty1212

yes A and C

- anonymous

An isomorphism of a ring is both an epimorphism and ________________
Monomorphism
Endomorphism
Automorphism
homomorphism

- anonymous

i think it is homomorphism

- misty1212

i am not sure what "homomorphism" of a ring means,
a homo from on ring to another?

- misty1212

isomorphism means a homomorphism that is both injective and surjective, or in this language "epi" and "mono"

- misty1212

if it is a epimorphism, it is already a homomorphism, don't pick that one

- anonymous

waw. you are good

- misty1212

ok actually i was not being precise
epi is not exactly surjective and mono is not exactly injective, but you can think of them that way

- anonymous

ok. which means Monomorphism is the answer

- misty1212

yes

- anonymous

thanks...
A endomorphism of a ring R is a _________ of R into itself

- misty1212

iso

- anonymous

Monomorphism
Endomorphism
Automorphism
homomorphism

- anonymous

does are the options

- misty1212

scratch that. go with homo

- anonymous

ok

- misty1212

i gotta run, good luck

- anonymous

Let R and S be rings and
ϕ:R→S
be an isomorphism, the
ϕ
is __________________

- anonymous

monomorphism
endomorphism
Automorphism
homomorphism

- anonymous

hello @ikram002p please help

- ikram002p

it should be homomorphism its the condition of being isomorphic

- ikram002p

why dont u start a new question so i would be able to help ?

- anonymous

ok. thanks

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