204F Maxim Doucet Hall
Ph.D. 1968 Texas A & M University
M.S. 1962 Texas A & M University
B.A. 1960 Texas A & M University
I joined the UL Lafayette faculty in 1968 and was one of the developers of the then new Ph.D. program, which began in 1968-69. I have been active in the Ph.D. program ever since. Thirteen students have written Ph.D. dissertations under my direction, the first finishing in 1973, with a dissertation in computational near-ring theory, and the most recent in 2011, with a dissertation in ring theory. My research interests have included: near-rings, rings, semirings, universal algebra, groups, semigroups, operational calculus, equivalents of the axiom-of-choice, ordinary differential equations, operational calculus, biomathematics, and the history of mathematics, with publication in each of these areas. Most recently my main research interest and publications have been on semigroups arising from rings. In 1980 I was a research fellow at NASA and in the late 1980's to 1995 was a consultant for a major oil company. In 1976 I received a UL Lafayette Distinguish Professor award. Although I retired from full time duties in 2004, as an emeritus professor, I have stayed active in research and teaching. Since 2004 three doctoral students have done dissertation research under my direction, almost every Spring semester I teach our History of Mathematics course, and occasionally have students do individual study courses with me. I have continued to be a member of the UL Lafayette graduate faculty and am active in our department's graduate program. At present I am a reviewer for A.M.S. Mathematical Reviews and for MAA book reviews.
Selected research publications:
- Negatively ordered semigroups (with R. P. Tucci), JP Journal of Algebra, Number Theory and Applications,30 (2013), 81-97.
- Generalized primary rings (with C. Gorton and R. Tucci), International Electronic Journal of Algebra, 12 (2012), 116-132.
- Rings whose semigroup of right ideals is J-trivial (with R. Tucci), International Electronic Journal of Algebra, 10 (2011), 151-161.
- Weak regularity in semigroups (with R. Tucci), JP Journal of Algebra, Number Theory, and Applications, 19 (2010), 1-12.
- Right weakly regular semigroups (with R. Tucci), JP Journal of Algebra, Number Theory, and Applications, 17 (2010), 27-40.
- Right weakly regular rings - A survey (with R. Tucci), Rings and Module Theory, Proc. Int. Conf. on Rings and Module Theory, T. Albu et.al (eds), Birkhauser, (2010), 115-123.
- Semigroups of ideals of right weakly regular rings (with R. Tucci and K. Kosler), Journal of Algebra, Number Theory, and Applications, 15 (2009), 89-100.
- The semigroup of right ideals of a ring (with R. Tucci),Math. Pannon., 18 (2007), 19-26
- Ideals in distributively generated nearrings (with G. Mason), Publ. Math. Debrecen, 69 (2006), 121-135
- Convolution algebras arising from Strum-Liouville transforms and applications (with J. Huffman), International J. Math. and Math. Sci., 27 (2001), 221-228.