“Rashid ZaareNahandi”
IPM Positions 

Non Resident Researcher (nonresident), School of Mathematics
(2002  2003 ) 

Past IPM Positions 

Associate Researcher (nonresident), School of Mathematics
(2000  2001) Student Researcher (nonresident), School of Mathematics (1997  2000) 

Non IPM Affiliations 

Assistant Professor of IASBS, Zanjan  
Research Interests 

Algebric Geometry, Commutative Algebra  
Research Activities 

Let I be a an ideal of the polynomial ring S=k[X_{1},?,X_{n}]
generated by squarefree monomials. A simplicial complex D_{I}
can be associated to the ring S/I. In this manner S/I is called StanleyReisner
ring and some of its invariants as Hilbert series and hvector and Betti
numbers, and primary decomposition of the ideal I can be deduced by
combinatorial computations in D_{I}.
Let X be a matrix of linear forms in the ring S. Let I_{t}(X) be the ideal generated by all tminors of X. Free complexes as EagonNorthcott complex is associated to the quotient ring over ideal of maximal minors of X. StanleyReisner rings and determinantal rings are widely studied by mathematicians. In this project, we aim to make a connection between these two subjects. First we determine StanleyReisner rings which can be regarded as a determinantal ring, and vise versa. For example ideal of tminors of a pluricirculant matrix after a linear change of coordinates, is a monomial ideal and has a simplicial complex. And, the StanleyReisner ideal generated by < _{1}chain monomials of degree t, is a determinantal ideal, were, we say a monomial X_{i1}?X_{is} is a < _{1}chain monomial if i_{j}+1 < i_{j+1} for all 1 ? j ? s. References


Present Research Project at IPM 

Relations between StanleyReisner and determinantal rings  
Related Papers 
1.  Rash. ZaareNahandi and Rah. ZaareNahandi The minimal free resolution of a class of squarefree monomial ideals J. Pure Appl. Algebra 189 (2004), 263278 [abstract] 
2.  Rah. ZaareNahandi and Rash. ZaareNahandi Gr·· obner basis and free resolution of the ideal of 2minors of A 2×n matrix of linear forms Comm. Algebra 28 (2000), 44334453 [abstract] 
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