In the first chapter some basic notions and results from
commutative algebra are being introduced. In the second chapter we
present new results related to sequentially Cohen Macaulay, pretty
clean and Stanley ideals. Let I be a monomial ideal of the poly-
nomial ring S. We show that S=I is sequentially Cohen-Macaulay if
and only if S=I is pretty clean. In particular, if S=I is
sequentially Cohen- Macaulay then I is a Stanley ideal. Chapter 3
includes some results related to Stanley Conjecture. We define nice
partition of the multicomplex associated to a Stanley ideal. In the
main result we show that if the multicomplex associated to monomial
ideal I has a nice partition then the multicomplex associated to
polarized ideal Ip has a nice partition. Fourth and last chapter
deals with the regularity of ideals of Borel type. We have proved
that the regularity of monomial ideals whose associated prime
ideals are totally ordered by inclusion is linearly bounded.
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