Uniformly 2-absorbing primary ideals of commutative rings

TL;DR

This paper introduces and explores the properties of uniformly 2-absorbing primary ideals in commutative rings, a new boundedness variant of existing ideals, including special cases with examples and properties.

Contribution

It defines the concept of uniformly 2-absorbing primary ideals and investigates their properties and specific subclasses within commutative rings.

Findings

Introduction of uniformly 2-absorbing primary ideals

Characterization and properties of these ideals

Examples and special subclasses analyzed

Abstract

In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative rings. Then we investigate some properties of uniformly 2-absorbing primary ideals of commutative rings with examples. Also, we investigate a specific kind of uniformly 2-absorbing primary ideals by the name of "special 2-absorbing primary ideals".