November 8, 2025

Square-difference factor absorbing primary ideals of commutative rings

Key Points

Properties of square-difference factor absorbing primary ideals are examined and clarified, revealing their rich structural characteristics.
Key characterizations show that these ideals satisfy certain algebraic conditions in commutative rings, enhancing their theoretical significance.
Analysis of various examples illustrates the broad applicability of these findings in mathematical contexts involving ideal theory in ring extensions.
The work emphasizes the importance of square-difference factor absorbing primary ideals, calling for further exploration in ring theory.

Abstract

Let Formula: see text be a commutative ring with identity. A proper ideal Formula: see text of a ring Formula: see text is called a square-difference factor absorbing primary ideal of Formula: see text if for Formula: see text, whenever Formula: see text, then Formula: see text or Formula: see text. Several characterizations and properties of this class of ideals are presented.Various examples are provided to illustrate the obtained results and demonstrate the applicability of our findings. Furthermore, the properties of this class of ideals are investigated in extensions of rings.

Square-difference factor absorbing primary ideals of commutative rings

Key Points

Abstract

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