Rees algebra

In commutative algebra, the Rees algebra or Rees ring of an ideal I in a commutative ring R is defined to be

${\displaystyle R[It]=\bigoplus _{n=0}^{\infty }I^{n}t^{n}\subseteq R[t].}$

The extended Rees algebra of I (which some authors^[1] refer to as the Rees algebra of I) is defined as

${\displaystyle R[It,t^{-1}]=\bigoplus _{n=-\infty }^{\infty }I^{n}t^{n}\subseteq R[t,t^{-1}].}$

This construction has special interest in algebraic geometry since the projective scheme defined by the Rees algebra of an ideal in a ring is the blowing-up of the spectrum of the ring along the subscheme defined by the ideal.^[2]