On Weakly 1-Absorbing Primary Ideals of Commutative Rings
Ayman Badawı, Ece Yetki̇n Çeli̇kel
Abstract
Let [Formula: see text] be a commutative ring with [Formula: see text]. We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal [Formula: see text] of [Formula: see text] is said to be weakly 1-absorbing primary if whenever nonunit elements [Formula: see text] and [Formula: see text], we have [Formula: see text] or [Formula: see text]. A number of results concerning weakly 1-absorbing primary ideals are given, as well as examples of weakly 1-absorbing primary ideals. Furthermore, we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.
Topics & Concepts
MathematicsIdeal (ethics)Primary idealCommutative ringGeneralizationRing (chemistry)Commutative propertyPure mathematicsPrimary (astronomy)Maximal idealSemiprime ringCombinatoricsPrincipal ideal ringMathematical analysisPhysicsQuantum mechanicsChemistryEpistemologyPhilosophyPrime (order theory)Organic chemistryRings, Modules, and AlgebrasCommutative Algebra and Its ApplicationsAdvanced Topics in Algebra