In mathematics, Lazard's universal ring is a ring introduced by Michel Lazard in Lazard (1955) over which the universal commutative one-dimensional formal group law is defined.
There is a universal commutative one-dimensional formal group law over a universal commutative ring defined as follows.
At first sight it seems to be incredibly complicated: the relations between its generators are very messy.
However Lazard proved that it has a very simple structure: it is just a polynomial ring (over the integers) on generators of degree 1, 2, 3, ..., where
Hence, topologists commonly regrade the Lazard ring so that
, because the coefficient ring of complex cobordism is evenly graded.