The set of germs of complex-valued functions forms a commutative ring. For example, to multiply (f,p) and (g,p), take two representatives f and g defined on a common neighborhood multiply them ...The set of germs of complex-valued functions forms a commutative ring. For example, to multiply (f,p) and (g,p), take two representatives f and g defined on a common neighborhood multiply them and then consider the germ (fg,p). Similarly, (f,p)+(g,p) is defined as (f+g,p). It is easy to check that these operations are well-defined.
