MATH 543 Commutative Algebra I

Commutative rings. Prime ideals and maximal ideals. Nilradical and Jacobson radical. Operation on ideals. Modules over commutative rings. Nakayama Lemma.Tensor product of modules.Restiriction and exlension of scalars. Exactness property of tensor product. Rings and modules of tractions. Local properties. Exlended and contracled ideals in rings of tractions.