Categoria: didattica algebra 4 2014-2015

Definition of modules, abelian groups as Z-modules, ideals as R-modules, submodules, quotient modules, morphism of modules, in R-mod is true invertible iff bijective but not true inj iff has left inverse or surj iff has right inverse, I II and III omomorphism theorem for modules, definition of direct sum and direct product of a generic family of modules, generating set, linear indepence, basis, free module, A^n is a free module for all n, Z_n is finitely generated but not free over Z, Q is neither finitely generated neither free over Z.

In our first lecture we recall previous notions about rings and ideals: definitions, eucliden rings, PID, UFD, irreducible and prime elements, ideals, prime and maximal ideals, nilpotent elements, I II and III omomorphism theorem for ideals, ideals of Z[i]/(2+i), the nipotent elements are the intersection of all prime ideals, definition of the Jacobson radical.