A poster presented at Computer Science Logic and 8th Kurt Gödel Colloquium, Vienna, Austria $25^{th} – 30^{th}$ August 2003. I introduce a class of commutative $f$-rings with strong unit and with a sort of weak divisibility property, called $f$-quasifields, and show that the categories of L$\Pi_q$-algebras and of $f$-quasifields are equivalent.