Elementary Proofs of the Wedderburn-Artin Theorem

Meltem Güllüsaç, Hikmet Burak Özcan and Sedef Taşkın, Dokuz Eylül University.
Date: 2nd of August, 2017, Wednesday, Time: 09:30 – 17:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: We shall present three proofs of the Wedderburn-Artin Theorem. In the first proof for non-unital rings, we follow Szele’s article [1], firstly proving the Density Theorem. In the second proof for unital rings, we follow Nicholson’s article [2]. Both of these proofs are for semiprime right or left artinian rings. In the third proof, we follow Section 3 Structure of Semisimple Rings from the book [3] by Lam. All proofs are elementary.
[1] Szele, T., Simple proof of the Wedderburn-Artin structure theorem, Acta Mathematica Hungarica, 5(1-2), 101-107, 1954.
[2] Nicholson, W. K., A Short Proof of the Wedderburn Artin Theorem, New Zealand Journal of Mathematics, 22, 83-86, 1993.
[3] Lam, T. Y. A First Course in Noncommutative Rings. 2nd edition. Springer, 2001.