Question

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

Answer 1

@misty1212

Answer 2

is the question asking for the identity matrix?

Answer 3

YES

Answer 4

it is the usual one

Answer 5

HMM.

Answer 6

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

Answer 7

yeah that one

Answer 8

OK

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

OK MA. HAVE SOME MORE...

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

yes A and C

Answer 25

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

Answer 26

i think it is homomorphism

Answer 27

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

Answer 28

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