Neovim lua module not found even though it exist

Question

I have structured my neovim config files like this

~/.config/nvim
├── init.lua
└── lua
    └── [username]
        ├── core
        │   └── options.lua
        ├── init.lua
        └── plugins

These are the contents of my files

-- init.lua

require("[username]")

-- ./lua/[username]/init.lua

print("hello world")
require("core.options")

-- ./lua/[username]/core/options.lua

local opt = vim.opt -- aliasing

-- line number
opt.number = true

-- tabs & intendation
opt.tabstop = 4
opt.shiftwidth = 4
opt.expandtab = true
opt.autoindent = true

-- search
opt.ignorecase = true
opt.smartcase = true

-- appearance
opt.termguicolors = false
opt.background = "dark"

When I open neovim, I get this error

hello world
Error detected while processing /home/[username]/.config/nvim/init.lua:
E5113: Error while calling lua chunk: /home/[username]/.config/nvim/lua/[username]/init.lua:2: module 'core.options' not found:
        no field package.preload['core.options']
        no file './core/options.lua'
        no file '/usr/share/luajit-2.1.0-beta3/core/options.lua'
        no file '/usr/local/share/lua/5.1/core/options.lua'
        no file '/usr/local/share/lua/5.1/core/options/init.lua'
        no file '/usr/share/lua/5.1/core/options.lua'
        no file '/usr/share/lua/5.1/core/options/init.lua'
        no file './core/options.so'
        no file '/usr/local/lib/lua/5.1/core/options.so'
        no file '/usr/lib/x86_64-linux-gnu/lua/5.1/core/options.so'
        no file '/usr/local/lib/lua/5.1/loadall.so'
        no file './core.so'
        no file '/usr/local/lib/lua/5.1/core.so'
        no file '/usr/lib/x86_64-linux-gnu/lua/5.1/core.so'
        no file '/usr/local/lib/lua/5.1/loadall.so'
stack traceback:
        [C]: in function 'require'
        /home/[username]/.config/nvim/lua/[username]/init.lua:2: in main chunk
        [C]: in function 'require'
        /home/[username]/.config/nvim/init.lua:1: in main chunk
Press ENTER or type command to continue

Answer 1

The solution was to change core.options to [username].core.options, since every require call in Lua looks for the file from the lua/ directory.

The reason is not completely clear to me yet. But a simple reason would be, as @Tae said in comments,

This is how Lua works.

I believe documentation of Lua require function can shed some light.

If someone can explain it better, please do.