| Course objectives: |
| Combinatorial aspects of algebra, introduction to the theory of rings |
| Course content and structure: |
| Polynomials in many variables, Hilbert’s Nullstellensatz. Symmetric polynomials. Noncommutative rings: Wedderburn-Artin Theory, Jacobson radical theory, prime and semiprime rings. local and semilocal rings. Short introduction to lattice theory. Linear algebra in lattices. Matrix algebras: Cayley-Hamilton theorem, Amitsur-Levitzki theorem and directed graphs |
| Evaluation method: |
| short presentation of a given subject |
| Required reading: 1. T.Y. Lam: A first course in noncommutative rings, Springer GTM, 2. M. Nagata: Local rings, Wiley, 3. G. Gratzer: Lattce Theory, Springer |
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| Suggested reading: |
| L.H. Rowen: Ring Theory Vols I., II, Academic Press |
