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On weakly 1-absorbing prime ideals

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Koç et al. - 2021 - On weakly 1-absorbing prime ideals.pdf (213.7 KB)

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2021-03-14

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SPRINGER-VERLAG ITALIA SRL

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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.

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Weakly prime ideal, 1-absorbing prime ideal, Weakly 2-absorbing ideal, Weakly 1-absorbing prime ideal, Trivial extension, Rings of continuous functions

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https://hdl.handle.net/11424/243429

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