2NF decomposition + database normalization
There's a little aphorism that goes:


The key (1NF)
The whole key (2NF)
And nothing but the key (3NF)


. . . So help me Codd

In your example we can assume 1NF to begin with as the relational structure doesn't imply any repeating groups within the row (i.e. no D1, D2, D3  etc.).


  R = {a, b, c, d, e, f, g} F = {AB --> C, A --> DE, B --> F, F --> GH,
  D --> IJ }


2NF deals with 'the whole key' - if you have a composite key and some members of the relation are dependent on a part of that key then they should be split off into their own relations.  In your case: 


R1 = AB --> C is in 2NF as 'AB' is 'the whole key'
R2 = A --> DEIJ is 2NF but not 3NF as A --> DE, but A --> IJ is not 3NF as the real dependency of I and J is D --> IJ.  D is not a key of this relation (A --> DEIJ), so A --> IJ violates the 'nothing but the key' princple of 3NF.
R3 = B --> FGH is in 2NF but not 3NF as B --> F is a correct relation and F is dependent on the entirety of the key 'B'.  However, B --> GH is not in 3NF as the correct relation is F --> GH.  B --> GH violates the 'nothing but the key' principle, as G ahd H are correctly dependent on the non-key attribute F.


Your decomposition to 2NF is correct.  Decomposition to 3NF requires taking the non-key attributes that have their own dependencies into separate relations.

The relation in 3NF would look like:


R1 = AB --> C
R2 = A --> DE (I and J are dependent on the non-key attribute D)
R3 = B --> F (G and H are dependent on the non-key attribute F)
R4 = D --> IJ
R5 = F --> GH