## anonymous one year ago let A=M2(Z) be the ring of 2×2 integral matrices the identity of A, IA

1. anonymous

@misty1212

2. misty1212

is the question asking for the identity matrix?

3. anonymous

YES

4. misty1212

it is the usual one

5. anonymous

HMM. |dw:1434206105315:dw|

6. misty1212

$\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}$

7. misty1212

yeah that one

8. anonymous

OK

9. anonymous

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

10. misty1212

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

11. misty1212

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

12. anonymous

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

13. misty1212

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

14. misty1212

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

15. anonymous

OK MA. HAVE SOME MORE...

16. misty1212

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

17. anonymous

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

18. 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

19. misty1212

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

20. anonymous

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

21. 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

22. anonymous

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

23. misty1212

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

24. misty1212

yes A and C

25. anonymous

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

26. anonymous

i think it is homomorphism

27. misty1212

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

28. misty1212

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

29. misty1212

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

30. anonymous

waw. you are good

31. 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

32. anonymous

ok. which means Monomorphism is the answer

33. misty1212

yes

34. anonymous

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

35. misty1212

iso

36. anonymous

Monomorphism Endomorphism Automorphism homomorphism

37. anonymous

does are the options

38. misty1212

scratch that. go with homo

39. anonymous

ok

40. misty1212

i gotta run, good luck

41. anonymous

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

42. anonymous

monomorphism endomorphism Automorphism homomorphism

43. anonymous

44. ikram002p

it should be homomorphism its the condition of being isomorphic

45. ikram002p

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

46. anonymous

ok. thanks