Commutative Algebra - Hacen, ZELACI (Université of eloued جامعة الوادي, 2025)
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.
Une publication pédagogique destinée aux étudiants de première année de master en mathématiques
Keywords: Commutative algebra; commutative rings; ideals; modules; Noetherian rings; localization; Hilbert’s Nullstellensatz; al- gebraic geometry; algebraic number theory; topology; primary de- composition; integral closures; graded rings.