An ideal I in a commutative Noetherian ring R is called normally torsion-free if Ass(R)(R/I-k) subset of 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.
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