Hello,
I would like to get the address of the 2nd element of an array called B
It works with an immediate number:

mov di, offset B[1]

but it does not like this:

mov al, 1
mov di, offset B[al]

I checked in emu8086, di contains simply the offset of B, al is ignored.
What is the logic behind of it?

in real mode not all registers can be used as indexing. also, displacement is 16-bit and must be summed with 16-bit numbers also

try this:
mov bx,1
lea di,[B + bx]

(fasm syntaxis)

btw, this will place byte from array into al, not its offset:
mov al,[B + bx]

i have use al instead di here, because di is 16-bit register and not designed to work with 8-bit values, as i see your array is sequence of bytes

Thank you, I will try that! Is it not a problem that a 16 bit reg (bx) is forced into a 8 bit reg (al)?
mov al,[B + bx]

As shoorick said, mov al, [B+bx] puts the byte at the address B+bx into al, not the address of that byte. Use lea instruction if you want to load the address.