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Polynomial identity ring
In
mathematics, in the subfield of
ring theory, a ring
R is a
polynomial identity ring if there is, for some
N > 0, an element
P other than 0 of the
free algebra, Z<
X1,
X2, ...,
XN>, over the
ring of integers in
N variables
X1,
X2, ...,
XN such that for all
N-
tuples r1,
r2, ...,
rN taken from
R it happens that