Introduction to Commutative Algebra is a commutative algebra textbook written by M. F. Atiyah and I. G. Macdonald. It deals with elementary concepts of commutative algebra such as noetherian modules, primary decomposition, integral dependence, and dimension theory. In abstract algebra, commutative algebra studies commutative rings, their ideals, and modules based on such rings; and of fields and their algebras. ... Sir Michael Francis Atiyah, OM (born 22 April 1929) is a mathematician who was born in London. ... In abstract algebra, an Noetherian module is a module that satisfies the ascending chain condition on its submodules, where the submodules are partially ordered by the inclusion. ... In mathematics, the Lasker-Noether theorem provides a vast generalization of the fundamental theorem of arithmetic to embrace the rings of algebraic geometry. ... Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ...

(Hardcover 1969, ISBN 0201003619) (Paperback 1994, ISBN 0201407515)