Stanley Conjecture and Regularity on Monomial Ideals : Stanley conjecture, Janet's Algorithm and Regularity on Monomial Ideals

ISBN-13: 9783838324784 / Angielski / Miękka / 2009 / 60 str.

Imran Anwar

Opis

In the first chapter some basic notions and results from commutative algebra are being introduced along with a description on the progress towards the Stanley s conjecture. In the second chapter, we have discussed the Stanley s conjecture for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we have presented that the monomial ideals with all associated primes of height two, are Stanley ideals. Moreover, we have introduced the Janet s algorithm for the Stanley decomposition of a monomial ideal and discussed the Janet s algorithm for the squarefree Stanley decomposition of squarefree monomial ideal. We conclude the chapter with the discussion of the Janet s algorithm for the partition of a simplicial complex. In the third and last chapter, we have discussed the regularity of monomial ideals in a polynomial ring in n variables, whose associated prime ideals are totally ordered by inclusion.

O autorze

I received my PhD in 2008 from Abdus Salam School of Mathematical sciences, G.C. University, Lahore, Pakistan, where I was the student of Prof. Dorin Popescu and, unofficially, Prof. Juergen Herzog. My area of interest is Commutative Algebra. Currently, I am teaching Mathematics in COMSATS Institute of Information Technology, Lahore.