Abstract:
The aim of this thesis is to explore the algebraic properties of square-free monomial
ideals with quasi-linear quotients. The concept of quasi-linear quotients has been
introduced in [1]. We discuss the graded-free resolutions of square-free monomial
ideals in R = k[x1, . . . , xn], with quasi-linear quotients. We show that a square-free
monomial ideal with quasi-linear quotients accept the quasi-linear free resolution.
Also, we discuss their betti numbers and give bounds on their projective dimension
and depth. We show that if I admits a quasi-linear quotients then so does I<t>.