In our first lecture we recall previous notions about rings and ideals: definitions, irreducible and prime and nilpotent elements (in particular in polynomial rings); ideals, prime and maximal ideals; quotient rings and bijection between ideals; I II and III omomorphism theorem for ideals; eucliden rings, PID, UFD; ideals of and
, the nipotent elements are the intersection of all prime ideals, definition of the Jacobson radical (in A[x] the Jacobson radical is the same as the nilpotents), definition of the radical of an ideal, prove that the radical of I is the intersection of all primes containing I, idempotent elements, Pierce decomposition, Boolean rings (Boolean domain is Z_2, every prime ideal is maximal, etc).
Prima lezione: 3/3/2016
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