Some algebraic Invariants of the residue class rings of the edge ideals of perfect semiregular trees

Abstract

Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, then we give precise formulas for values of depth, Stanley depth, projective dimension, regularity and Krull dimension of S/I.

KEYWORD:

• Depth
• Krull dimension
• monomial ideal
• perfect n-ary tree
• perfect semiregular tree
• projective dimension
• regularity
• Stanley depth

2020MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13C15
• Secondary: 13P10
• 13F20

Acknowledgments

We would like to express our sincere gratitude to anonymous referee for providing us with useful comments and valuable suggestions regarding an early version of the manuscript.