anonymous
  • anonymous
let A=M2(Z) be the ring of 2×2 integral matrices the identity of A, IA
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
misty1212
  • misty1212
is the question asking for the identity matrix?
anonymous
  • anonymous
YES

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misty1212
  • misty1212
it is the usual one
anonymous
  • anonymous
HMM. |dw:1434206105315:dw|
misty1212
  • misty1212
\[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\]
misty1212
  • misty1212
yeah that one
anonymous
  • anonymous
OK
anonymous
  • anonymous
Let G be a group and H1 , H2 normal subgroups of .one of these is a normal subgroup of G
misty1212
  • misty1212
whew i thought it was going to be some hard ring question, not a nice easy one
misty1212
  • misty1212
you lost me there, was it perhaps a copy and paste fail?
anonymous
  • anonymous
1)H1 INTERCEPT H2 2)H1 UNION H2 3)H1-H2 4)AXB
misty1212
  • 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
  • misty1212
depending of course on what your definition of a normal subgroup is there are a couple
anonymous
  • anonymous
OK MA. HAVE SOME MORE...
misty1212
  • misty1212
wait, you don't have to prove it, just pick one?
anonymous
  • anonymous
If R and R'are rings, a mapping ϕ:R→R′ ring ho morphism if any of these happen ∀a,b,∈R
anonymous
  • 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
  • misty1212
wow an abstract algebra class with multiple guess questions? no proofs just pick?
anonymous
  • anonymous
IM VERY CONFUSE and the book i have does note contain all these.
misty1212
  • 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
  • anonymous
yes. i thought as much. it is multiplication and addition . right?
misty1212
  • misty1212
or just read the top line here https://en.wikipedia.org/wiki/Ring_homomorphism
misty1212
  • misty1212
yes A and C
anonymous
  • anonymous
An isomorphism of a ring is both an epimorphism and ________________ Monomorphism Endomorphism Automorphism homomorphism
anonymous
  • anonymous
i think it is homomorphism
misty1212
  • misty1212
i am not sure what "homomorphism" of a ring means, a homo from on ring to another?
misty1212
  • misty1212
isomorphism means a homomorphism that is both injective and surjective, or in this language "epi" and "mono"
misty1212
  • misty1212
if it is a epimorphism, it is already a homomorphism, don't pick that one
anonymous
  • anonymous
waw. you are good
misty1212
  • 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
  • anonymous
ok. which means Monomorphism is the answer
misty1212
  • misty1212
yes
anonymous
  • anonymous
thanks... A endomorphism of a ring R is a _________ of R into itself
misty1212
  • misty1212
iso
anonymous
  • anonymous
Monomorphism Endomorphism Automorphism homomorphism
anonymous
  • anonymous
does are the options
misty1212
  • misty1212
scratch that. go with homo
anonymous
  • anonymous
ok
misty1212
  • misty1212
i gotta run, good luck
anonymous
  • anonymous
Let R and S be rings and ϕ:R→S be an isomorphism, the ϕ is __________________
anonymous
  • anonymous
monomorphism endomorphism Automorphism homomorphism
anonymous
  • anonymous
hello @ikram002p please help
ikram002p
  • ikram002p
it should be homomorphism its the condition of being isomorphic
ikram002p
  • ikram002p
why dont u start a new question so i would be able to help ?
anonymous
  • anonymous
ok. thanks

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