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This research aims to define and analyze (3, 1)-absorbing primary ideals and their interrelations with established ideal classes.

June 4, 2026Open MathematicsOpen Access

On (3, 1)-absorbing primary ideals in commutative rings

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The paper explores the properties of (3, 1)-absorbing primary ideals in commutative rings, suggesting new insights.

This research aims to define and analyze (3, 1)-absorbing primary ideals and their interrelations with established ideal classes.
Introduced the concept of (3, 1)-absorbing primary ideals in commutative rings.
Established characterizations and relationships with classical 1-absorbing primary ideals.
Examined connections with other absorption-type ideals and classified them in pullback rings.
Characterizations of (3, 1)-absorbing primary ideals were established, showing new properties.
Demonstrated specific conditions under which (3, 1)-absorbing primary ideals coincide with 1-absorbing ideals.
Classified (3, 1)-absorbing primary ideals in pullback rings using explicit radical descriptions.

Abouhalaka et al. (2026) studied this question.

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