Graphical properties of the bipartite graph of Spec(Z[x])\{0}

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Christina Eubanks-Turner¹  Aihua Li² 

[1] Department of Mathematics, Loyola Marymount University;Department of Mathematical Sciences, Montclair State University

关键词: Bipartite graph;    Prime spectrum;    Poset;    Ring theory;   

DOI  :  10.13069/jacodesmath.66836

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Consider Spec(Z[x]), the set of prime ideals of Z[x] as a partially ordered set under inclusion. Byremoving the zero ideal, we denote GZ = Spec(Z[x])\{0} and view it as an infinite bipartite graph withthe prime ideals as the vertices and the inclusion relations as the edges. In this paper, we investigatefundamental graph theoretic properties of GZ. In particular, we describe the diameter, circumference,girth, radius, eccentricity, vertex and edge connectivity, and cliques of GZ. The complement of GZ isinvestigated as well.

【 授权许可】

CC BY