New upper bounds on the first and second Hilbert coefficients of a Cohen-Macaulay module over local ring are given. Characterizations provided for some to be attained. The characterizations given in terms series as well Castelnuovo-Mumford regularity associated graded module.

We determine the Castelnuovo-Mumford regularity of binomial edge ideals complement reducible graphs (cographs). For cographs with $n$ vertices maximum grows as $2n/3$. also bound by graph theoretic invariants and construct a family counterexamples to conjecture Hibi Matsuda.

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and...

In this paper we give a nice formula for the CastelnuovoMumford regularity of the Segre product of modules, under some suitable hypotheses. This extends recent results of David A. Cox, and Evgeny Materov (2009).

We study the initial ideal of binomial edge ideal in degree 2 ([in<(JG)]2), associated to a graph G. We computed dimension, depth, Castelnuovo-Mumford regularity, Hilbert function and Betti numbers of [in<(JG)]2 for some classes of graphs. AMS Mathematics Subject Classification (2010): 05E40, 16E30

The behaviour of Castelnuovo-Mumford regularity under “geometric” transformations is not well understood. In this paper we are concerned with examples which will shed some light on certain questions concerning this behaviour. One simple question which was open (see e.g. [R]) is: May the regularity increase if we pass to the radical or remove embedded primes? By examples, we show that this happe...