Gary F. Birkenmeier

Professor Emeritus
Algebra

204E Maxim Doucet Hall
337-482-6545
gary.birkenmeier@louisiana.edu

Ph.D. 1975 University of Wisconsin at Milwaukee (advisor, Edmund H. Feller)
M.S. 1973 University of Wisconsin at Milwaukee
B.S. 1968 Regis College

Prior to coming to the University of Louisiana at Lafayette in 1985, I worked at a variety of occupations which helped to shape my career. I was an engineering aide at Barber & Nichols Consulting Engineers, a programmer at Scientific Software Corporation, an infantry officer in the US Army, an assistant professor at Floyd Junior College, an assistant professor at Southeast Missouri State University, and an assistant professor at Kuwait University. Since being at UL Lafayette, I have had the opportunity to share my experience and passion for Mathematics with many students and faculty. As advisor for the Math Club, I initiated and encouraged students to solve journal problems, thus competing with individuals and teams worldwide. So far, I have supervised or jointly supervised 10 Ph.D. students and have written over 140 research papers and one advanced graduate level textbook with colleagues from here and around the world. My research has led to invitations to visit and collaborate or lecture in Austria, Canada, China, Czech Republic, Egypt, Hungary, India, Mexico, South Africa, South Korea, Thailand, Turkey, and throughout the USA.

My current research interests are Ring and Module Theory, Near-ring Theory, Radical Theory, Semigroup Theory, Groupoid Theory, Loop Theory, Coding Theory, and Universal Algebra. In ring theory my recent research is on on quasi-Baer rings and on structural decompositions especially triangular matrix representations. For module theory I am interested in decompositions arising from various generalizations of injectivity and/or projectivity. Much of my research in ring theory, near-ring theory, and semigroup theory centers around the concepts of primeness and nilpotency. In groupoid theory I study various identities including the left (or right) self distributive identity. Some of these results have been extended to rings and near-rings. Also I have investigated loops which are semidirect products of subgroups and group codes.

Selected research publications:

• Birkenmeier, Gary F. and Heider, Blaise J., Annihilators and extensions of idempotent-generated ideals, Comm. Algebra, 47 (2019) no. 3,1348--1375.
• Birkenmeier, Gary F. and Kara, Yeliz and Tercan, Adnan, A survey of rings satisfying annihilator or extending conditions on projection invariant ideals, Advances in algebra, Springer Proc. Math. Stat., 277 (2019),53--65.
• Birkenmeier, Gary F. and Lee, Enoch K. S., A survey of intrinsic extensions of rings, Advances in rings and modules, Contemp. Math., 715 (2018),69--88.
• Birkenmeier, G. F. and Ghirati, M. and Ghorbani, A. and Naghdi, A. and Taherifar, A.,Corrigendum to: When is a sum of annihilator ideals an annihilator ideal?, Comm. Algebra, 46 (2018) no. 10,4174--4175.
• Birkenmeier, Gary F. and Kara, Yeliz and Tercan, Adnan, $\pi$-Baer rings, J. Algebra Appl., 17 (2018) no. 2,1850029, 19.
• Birkenmeier, Gary F. and Kim, Jin Yong and Park, Jae Keol, Corrigendum and addendum to "Right primary and nilary rings and ideals" [J. Algebra 378 (2013) 133--152], J. Algebra, 486 (2017),417--421.
• Birkenmeier, Gary F. and Davis, Donald D., Quasi-Baer and biregular generalized matrix rings, J. Algebra Appl., 16 (2017) no. 4,1750067, 15.
• Birkenmeier, Gary F. and Tercan, Adnan and Yucel, Canan C., Projection invariant extending rings, J. Algebra Appl., 15 (2016) no. 7,1650121, 11.
• \'Anh, P. N. and Birkenmeier, G. F. and van Wyk, L., Idempotents and structures of rings, Linear Multilinear Algebra, 64 (2016) no. 10,2002--2029.
• Birkenmeier, Gary F. and Ryan, C. Edward, Module decompositions using pairwise comaximal ideals, Comm. Algebra, 44 (2016) no. 10,4200--4211.