University Studies 4-Fall 2012-Suggested Projects from October 25 meeting 

The proof of Theorem 2 (due to Wedderburn/Noether) is contained in the paper of Jacobson of 1937 which can be found as a link in the projects for the meeting of September 27

The proof of the module version of Theorem 2 is contained in the paper of Hochschild of 1942 which is also a link in the suggested projects for the meeting of September 27.

The proof of Theorem 3 (due to Zassenhaus/Cartan) is contained in the lecture notes of Meyberg of 1972 which can be found as a link in the projects for the meeting of October 4

The proof of the module version of Theorem 3 is contained in the paper of Hochschild of 1942 which is a link in the projects for the meeting of September 27, and of October 4.

The proof of Theorem 4 is contained in the paper of Jacobson of 1949 which can be found as a link in the projects for the meeting of October 4

The proof of the module version of Theorem 4 is contained in the paper of Jacobson of 1951 which is the first link below

In anticipation of our study of applications of nonassociative algebra, below are links to three papers on cryptography.

(Warning: I have not read these three papers yet so I don't know how accessible they are---stay tuned)

Jacobson 1951 (for module version of Theorem 4---See Theorem 9.1 in this paper) (pdffile)

"Quasigroups in cryptology"-V.A. Shcherbacov July 22, 2010-(31 pages) (pdffile)

"OTRU: A Non-Associative and High Speed Public Key Cryptosystem" -Ehsan Malekian, Ali Zakerolhosseini-IEEE (2009), 83-90 (pdffile)

"Non-associative algebraic system in cryptology. Protection against 'meet in the middle' attack"-Jozsef Denes and Tamas Denes-Quasigroups and Related Systems 8 (2001),7-14 (pdffile)