Commutative Algebra

Abstract

These lecture notes provide an introduction to commutative al- gebra for Master 1 students, focusing on commutative rings, ideals,

and modules. The course explores essential topics such as prime and

maximal ideals, localization, Noetherian rings, and Hilbert’s Null- stellensatz. We will also discuss concepts like primary decomposition

and integral closures. The goal is to equip students with a strong foundation in commutative algebra and its connections to algebraic geometry, number theory, and topology.