I have a problem with fasm. I write in my kernel mov eax,0x10001 (after going to pmode ang "use32"), then cli hlt and run it in bochs. In bochs log, there is EAX=00000001 (it is cut-off to 16bit). Then I decompiled it, and I see mov ax,0x0001
Why is that not what I written? Tried on small files (only this mov eax,0x10001 and still doesn't work)
Does someone know, what to do to get 32bit opcodes? Please, help[/code]

Make sure that you disassemble with the same bitness as you assembled it (32 in this case). Many disassemblers (like HIEW or BIEW, for quick example) disassemble flat binary files as "use16" by default.

I disasembled it with ndisasm (nasm package) and BOCHS (cli hlt just before it). And also BOCHS executes it as mov ax,0x0001 even if in protected mode.

So either it is the 16-bit protected mode, or you have assembled it to 16-bit (without "use32").

mov eax,0x10001 should assemble to 6 bytes in 16-bit mode and 5 bytes in 32-bit mode. Check it!