In
mathematics, especially in the field of
abstract algebra, a
polynomial ring or
polynomial algebra is a
ring (which is also a
commutative algebra) formed from the
set of
polynomials in one or more
indeterminates (traditionally also called
variables) with coefficients in another
ring, often a
field. Polynomial rings have influenced much of mathematics, from the
Hilbert basis theorem, to the construction of
splitting fields, and to the understanding of a
linear operator. Many important conjectures involving polynomial rings, such as
Serre's problem, have influenced the study of other rings, and have influenced even the definition of other rings, such as
group rings and
rings of formal power series.