On weakly 1-absorbing prime ideals - KOÇ, SUAT; TEKİR, ÜNSAL (SPRINGER-VERLAG ITALIA SRL, 2021)
This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity 1 not equal 0. A proper ideal P of A is said to be a weakly 1-absorbing prime ideal if for every nonunits x, y, z. A with 0 not equal xyz. P, then xy is an element of P or z is an element of 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.
Keywords: Weakly prime ideal; 1-absorbing prime ideal; Weakly 2-absorbing ideal; Weakly 1-absorbing prime ideal; Trivial extension; Rings of continuous functions