Normally torsion-freeness of monomial ideals under monomial operators

Abstract

An ideal I in a commutative Noetherian ring R is called normally torsion-free if ${\text{Ass}}_R(R/I^k)\subseteq {\text{Ass}}_R(R/I)$ for all positive integers k. In this article, by using some monomial operators, such as expansion, weighted, monomial multiple, monomial localization, contraction, and deletion, we introduce several methods for constructing new normally torsion-free monomial ideals based on the monomial ideals which have normally torsion-freeness.

Keywords:

• Associated primes
• monomial operators
• normally torsion-free ideals

2010 Mathematics Subject Classification:

• 13B25
• 13F20

Acknowledgments

The authors are deeply grateful to the referee for careful reading of the manuscript.

Additional information

Funding

Mirsadegh Sayedsadeghi was supported by the grant of Payame Noor University of Iran.