2020/05/20 by Koç, Suat, Tekir, Ünsal, Yıldız, Eda · 1 citation
#13A15 #13C05 #54C35 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.10365
This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity 1≠ 0. A proper ideal P of A is said to be a weakly 1-absorbing prime ideal if for each nonunits x, y, z ∈ A with 0≠ xyz ∈ P, then either xy ∈ P or z ∈ P. In addition to give many properties and characterizations of weakly 1-absorbing prime ideals, we also determine rings in which every proper ideal is weakly 1-absorbing prime. Furthermore, we investigate weakly 1-absorbing prime ideals in C(X), which is the ring of continuous functions of a topological space X.