IPM Positions

Non Resident Researcher (non-resident), School of Mathematics (2004 - 2005 )

Past IPM Positions

Associate Researcher (non-resident), School of Mathematics (1998 - 2004) Associate Researcher (non-resident), School of Mathematics (1996 - 1997) Associate Researcher (non-resident), School of Mathematics (1994 - 1995)

Research Activities

We shall carry out a further study of modules that satisfy one or both of the conditions weakly co-Hopfian, and generalized Hopfian. Recall that a module M over an associative ring R is called weakly co-Hopfian if any injective endomorphism of M is essential. We say M is generalized Hopfian if any subjective endomorphism is small. Many properties of weakly co-Hopfian modules have been investigated in [A. Haghany ,M. R.Vedadi, J.Algebra 243,765-779(2001)], while in a forthcoming paper [A. Ghorbani, A.Haghany, J.Algebra] generalized Hopfian modules will be dealt with. Our aim is to establish some duality like connections between weakly co-Hopfian modules and generalized Hopfian modules. Already we have some interesting results in the case that duals are taken with respect to a cogenerator or an injective cogenerator. We shall seek duality results of more general nature

Present Research Project at IPM

Some Duality -Like Connections for Modules

Related Papers

1.	A. Haghany and M. R. Vedadi Endoprime modules Acta Math. Hungar. 106 (2005), 89-99  [abstract]

2.	A. Ghorbani and A. Haghany Duality for weakly co-Hopfian and generalized Hopfin modules Comm. Algebra 31 (2003), 2811-2817  [abstract]

3.	A. Haghany Injectivity conditions over a formal triangular matrix ring Arch. Math. (Basel) 78 (2002), 268-274  [abstract]

4.	A. Haghany and K. Varadarajan IBN and related properties for rings Acta Math. Hungar. 94 (2002), 251-261  [abstract]

5.	A. Haghany and M. R. Vedadi Modules whose injective endomorphisms are essential J. Algebra 243 (2001), 765-779  [abstract]

6.	K. Varadarajan and A. Haghany Matricial repetitiveness and strong π-regularity of the ring of a Morita context Bull. Iranian Math. Soc. 26 (2000), 41-50  [abstract]

7.	A. Haghany and K. Varadarajan Study of modules over formal triangular matrix rings J. Pure Appl. Algebra 147 (2000), 41-58  [abstract]

8.	A. Haghany Hopficity and co-Hopficity for Morita contexts Comm. Algebra 27 (1999), 477-492  [abstract]

9.	A. Haghany On the torsion theories of Morita equivalent rings Period. Math. Hungar. 32 (1996), 193-197  [abstract]