Welcome to my homepage. Comments welcome; it is always under construction.

 
     
(October 2006, with my daughter Andrea)
Alina Duca  Visiting Assistant Professor
                     Vassar College
                     Department of Mathematics

Education            
                    PhD                                  University of Manitoba, Canada
                    M.Sc.                               Al.I.Cuza University, Romania
                    Bachelor's Degree         Al.I.Cuza University, Romania

Contact Information    
Email                   alduca@vassar.edu
Phone                  1 - 845 - 437 - 5523
Fax                      1 - 845 - 437 - 7544
Mailing address  Vassar College          
                             124 Raymond Ave., Box 25                                                                                                           Poughkeepsie, NY 12604
Office Hours:       Mondays 2:00 - 3:00
                              Wednesdays 8:30 - 10:00
                              Thursdays 2:00 - 3:00, and by appointment                                                      

Teaching (2007-2008)
Courses, Fall 2007        
Math 121. Single Variable Calculus
             Math 241. Probability Models


 Courses, Spring 2008   
Math 122. Single Variable Calculus
              Math 231. Topics in Geometry

            Math 399. Topics in Modern Algebra (Senior Independent Work)

Research Interests
My area of expertise is the the theory of rings and modules, and in particular I am interested in the injective modules over noetherian (non-commutative) rings. I am also investigating the model theoretic techniques that can be applied in a useful way to solve problems in module theory. More precisely, my doctoral thesis concentrated on explicitly describing  the internal structure of an arbitrary  indecomposable injective module E over a principal left and right ideal domain, based on analysis of its classical and elementary socle series. In addition, since the first Weyl algebra and related algebras of differential operators posses a faithful family of localizations which are principal left and right ideal domains, some of the basic algebraic structure of their wild injective modules are consequences of the above mentioned results.
 
Keywords and phrases: injective module, noetherian ring, socle series, elementary socle series, localization, Weyl algebra, rings of differential operators

Publications
1. Injective modules over a principal left and right ideal domain, with applications.PhD Thesis, University of Manitoba, 2007 (Advisor: T.G.Kucera)
2. The socle series of an injective modules over a principal left and right ideal domain. (submitted)
3. The elementary socle series of an injective modules over a principal left and right ideal domain. (submitted)
4. The bimodule structure of an injective module over a principal left and right ideal domain. (to be submitted)
5. Injective modules over the first Weyl algebra and related algebras. (in preparation)

Links
Alina Duca January 2008
Background courtesy of Eos Web Art