  The "neural code" is the way the brain characterizes, stores, and processes
information. Unraveling the neural code is a key goal of mathematical
neuroscience. Topology, coding theory, and, recently, commutative algebra are
some the mathematical areas that are involved in analyzing these codes. Neural
rings and ideals are algebraic objects that create a bridge between
mathematical neuroscience and commutative algebra. A neural ideal is an ideal
in a polynomial ring that encodes the combinatorial firing data of a neural
code. Using some algebraic techniques one hopes to understand more about the
structure of a neural code via neural rings and ideals. In this paper, we
introduce an operation, called "polarization," that allows us to relate neural
ideals with squarefree monomial ideals, which are very well studied and known
for their nice behavior in commutative algebra.
