Algebraic Properties of Powers of Edge Ideals of Vertex-Weighted Oriented Cycles  

作　　者：Hong Wang Guangjun Zhu Li Xu 

机构地区：[1]School of Mathematical Sciences,Soochow University,Suzhou,Jiangsu 215006,China

出　　处：《Algebra Colloquium》2023年第4期649-666,共18页代数集刊（英文版）

基　　金：This research is supported by the Natural Science Foundation of Jiangsu Province(BK20221353);the foundation of the Priority Academic Program Development of Jiangsu Higher Education Institutions.Finally,the authors would like to thank the referees who read the manuscript carefully and gave very helpful comments,which improved the paper both in mathematics and presentation.

摘　　要：Let t be any positive integer and I(C_(n)) the edge ideal of a vertex-weighted oriented n-cycle graph C_(n).We provide explicit formulas for the regularity and depth of I(C_(n))^(t).In particular,we find that the regularity of I(C_(n))^(t)is a linear function;Ass(I(C_(n))^(t),the set of associated prime ideals of I(C_(n))^(t),equals Ass(I(C_(n))^(t);and the depth of I(C_(n))^(t)is a constant for all.We also give some examples to show that these results are related to the direction selection of edges and the weight of vertices.

关 键 词：depth REGULARITY powers of an ideal vertex-weighted oriented cycles 

分 类 号：O15[理学—数学]