The four properties of the noun

Every Arabic ism carries four properties at once — definiteness, gender, number, and i'rab — and three of them you already use in English without thinking. “The kings” is definite, masculine, plural; “a book” is indefinite and singular. Arabic simply asks you to state these openly on the word. Only the fourth, i'rab — the changing case-ending — is genuinely new, and it is the one that unlocks how a sentence fits together.

From the free course The Language of Quran — Easier than English (Book 1) (LoQ1), taught by Ustad Muhammad Arjan Ali.

Do verbs and particles have the four properties too?

No — the four properties belong to the ism alone. Verbs carry their own information (tense, doer, action) and particles are fixed. That is one reason identifying the word type is always the first step in parsing.

Is there a shorthand for noting the four properties?

The course uses D/I for definiteness, mg/fg for gender, s./d./p. for number and R/N/J for i'rab. Four symbols fully describe any ism: الْحَمْدُ is D · mg · s. · R.