Gary F. Birkenmeier
Professor

Contact:
Office: 101 Foster
Phone: 337-482-6545
E-mail: gfb1127@louisiana.edu
Home page: not available

Degrees:
Ph.D. 1975 University of Wisconsin at Milwaukee
M.S. 1973 University of Wisconsin at Milwaukee
B.S. 1968 Regis College

Statement:
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:

• When some complement of a submodule is a summand (with Tercan, Adnan), Comm. Algebra, 35 (2007), 597--611.
• An essential extension with nonisomorphic ring structures (with Park, Jae Keol and Rizvi, S. Tariq), Algebra and its applications, Contemp. Math., 419 (2006), 29--48.
• Ring hulls and applications (with Park, Jae Keol and Rizvi, S. Tariq), J. Algebra, 304 (2006), 633--665.
• Annihilator conditions on polynomials II (with Huang, Feng-Kuo), Monatsh. Math., 141 (2004), 265--276.
• Radicals whose semisimple classes satisfy a generalised ADS condition (with Booth, G. L. and Groenewald, N. J.), Acta Math. Hungar., 102 (2004), 239--248.
• Triangular matrix representations of ring extensions (with J.K. Park), J. Algebra, 265 (2003), 457-477.
• Rings containing ideals with bounded index (with E.P. Armendariz and J.K. Park), Comm. Algebra, 30 (2002), 787-801.
• Modules in which every fully invariant submodule is essential in a direct summand (with B.J. Müller and S.T. Rizvi), Comm. Algebra, 30 (2002), 1395-1415.
• Supplementing radicals and decompositions of near-rings (with R. Wiegandt), Acta Math. Hungar., 94 (2002), 269-280.
• Near-ring extensions with a common ideal (with M. Farag and H.E. Heatherly), Publ. Math. Debrecen, 61 (2002), 603-612.
• The fully invariant extending property for abelian groups (with G. Calugareanu, L. Fuchs, and P.H. Goeters), Comm. Algebra, 29 (2001), 673-685.
• On class pairs and radicals (with N.J. Groenewald and W.A. Olivier), Comm. Algebra, 29 (2001), 5307-5328.
• Polynomial extensions of Baer and Quasi-Baer rings (with J.Y. Kim and J.K. Park), J. Pure and Appl. Algebra, 159 (2001), 25-42.
• Triangular matrix representations (with H.E. Heatherly, J.Y. Kim, and J.K. Park), J. Algebra, 230 (2000), 558-595.
• Pseudocomplements in the lattice of torsion classes (with R. Weigandt), Comm. Algebra, 26 (1998), 197-220.
• Homomorphisms on groups I. Distributive and d.g. near-rings (with H.E. Heatherly, and G. Pilz), Comm. Algebra, 25 (1997), 185-211.
• When does a supernilpotent radical essentially split-off?, J. Algebra, 172 (1995), 49-60.
• A connection between weak regularity and the simplicity of prime factor rings (with J. Y. Kim, and J. K. Park), Proc. Amer. Math. Soc., 122 (1994), 53-58.
• Is a semidirect product of groups necessarily a group? (with B. Davis, K. J. Reeves, and S. Xiao), Proc. Amer. Math. Soc., 118 (1993), 689-692.
• Rings with left self distributive multiplication (with H. E. Heatherly and T. Kepka), Acta Math. Hungar., 60 (1992), 107-114.
• Decompositions of Baer-like rings, Acta Math. Hung., 59 (1992), 319-326.
• Rings whose additive endomorphisms are ring endomorphisms (with H. E. Heatherly), Bull. Austral. Math. Soc., 42 (1990), 145-152.
• A generalization of FPF rings, Comm. Algebra, 17 (1989), 855-884.
• Operation inducing systems, (with H. E. Heatherly), Algebra Universalis, 24 (1987), 137-148.
• Quotient rings of rings generated by faithful cyclic modules, Proc. Amer. Math. Soc., 100 (1987), 8-10.
• Exponentiation and the identity X²Y=(XY)², Comm. Algebra, 13 (1985), 681-695.
• Indecomposable decompositions and the minimal direct summand containing the nilpotents, Proc. Amer. Math. Soc., 73 (1979), 11-14.
• Modules which are subisomorphic to injective modules, J. Pure Appl. Algebra, 13 (1978), 169-177.