Add to ORKGIn this thesis I introduce the concepts of arc ideals, unmixed digraphs, and Cohen-Macaulay digraphs, and study their algebraic and combinatorial properties by using commutative algebra and graph theory. The main results are the complete characterizations of the unmixed digraphs with δ > 0 and Cohen-Macaulay digraphs. The thesis consists of five chapters, which are organized as follows. Chapter 1 provides the algebraic backgrounds which are needed in the thesis with the aim of introducing the Cohen-Macaulay rings and Cohen-Macaulay modules. Chapter 2 presents the basic terminology and notion for graphs and digraphs, a short exposition of matching theory, and some relevant results on two types of digraphs: acyclic digraphs and transitive d...
Let G be a finite simple graph on [n] and I(G) ⊂ S the edge ideal of G, where S = K[x1,..., xn] is ...
In this dissertation \ud we study Cohen Macaulay monomial ideals with a given radical. Among \ud ...
. Numerical invariants which measure the Cohen--Macaulay character of homomorphisms ' : R ! S ...
It is shown in this paper how a solution for a combinatorial problem obtained from applying the gree...
In this article, we study the theory and properties of co-Cohen-Macaulay modules. We show, for examp...
For a positive integer k a class of simplicial complexes, to be denoted by CM(k), is introduced. Thi...
In this work we obtain the result that the complement of a $d$-tree is a Cohen-Macaulay graph. To do...
In this paper we study simplicial complexes as higher dimensional graphs in order to produce algebra...
Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal a...
This dissertation builds upon two well-known theorems: Macaulay's theorem on the Hilbert functions o...
We study the Cohen-Macaulay property of Rees algebras of modules of K¨ahler differentials. When the ...
In this thesis we \ud give a structure theorem for Cohen-Macaulay monomial ideals of \ud codim...
This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) ...
Abstract Let R = k[x1, . . . , xn], where k is a field. The path ideal (of length t ≥ 2) of a direct...
In this paper we introduce a new kind of graph associated with a commutative ring with identity, and...
Let G be a finite simple graph on [n] and I(G) ⊂ S the edge ideal of G, where S = K[x1,..., xn] is ...
In this dissertation \ud we study Cohen Macaulay monomial ideals with a given radical. Among \ud ...
. Numerical invariants which measure the Cohen--Macaulay character of homomorphisms ' : R ! S ...
It is shown in this paper how a solution for a combinatorial problem obtained from applying the gree...
In this article, we study the theory and properties of co-Cohen-Macaulay modules. We show, for examp...
For a positive integer k a class of simplicial complexes, to be denoted by CM(k), is introduced. Thi...
In this work we obtain the result that the complement of a $d$-tree is a Cohen-Macaulay graph. To do...
In this paper we study simplicial complexes as higher dimensional graphs in order to produce algebra...
Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal a...
This dissertation builds upon two well-known theorems: Macaulay's theorem on the Hilbert functions o...
We study the Cohen-Macaulay property of Rees algebras of modules of K¨ahler differentials. When the ...
In this thesis we \ud give a structure theorem for Cohen-Macaulay monomial ideals of \ud codim...
This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) ...
Abstract Let R = k[x1, . . . , xn], where k is a field. The path ideal (of length t ≥ 2) of a direct...
In this paper we introduce a new kind of graph associated with a commutative ring with identity, and...
Let G be a finite simple graph on [n] and I(G) ⊂ S the edge ideal of G, where S = K[x1,..., xn] is ...
In this dissertation \ud we study Cohen Macaulay monomial ideals with a given radical. Among \ud ...
. Numerical invariants which measure the Cohen--Macaulay character of homomorphisms ' : R ! S ...