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- W4220781380 abstract "Abstract In this paper, we introduce and study the notion of an 𝑆-weakly prime ideal which is a generalization of a weakly prime ideal. Let 𝐴 be a commutative ring and 𝑆 a multiplicative set of 𝐴. We define a proper ideal 𝑃 of 𝐴 to be 𝑆-weakly prime if there exists <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>s</m:mi> <m:mo>∈</m:mo> <m:mi>S</m:mi> </m:mrow> </m:math> sin S such that, for all <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi>a</m:mi> <m:mo>,</m:mo> <m:mi>b</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>A</m:mi> </m:mrow> </m:math> a,bin A with <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mn>0</m:mn> <m:mo>≠</m:mo> <m:mrow> <m:mi>a</m:mi> <m:mo></m:mo> <m:mi>b</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>P</m:mi> </m:mrow> </m:math> 0neq abin P , then <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi>s</m:mi> <m:mo></m:mo> <m:mi>a</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>P</m:mi> </m:mrow> </m:math> sain P or <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi>s</m:mi> <m:mo></m:mo> <m:mi>b</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>P</m:mi> </m:mrow> </m:math> sbin P . We describe the behavior of an 𝑆-weakly prime property across various ring-theoretic constructions such as direct product, homomorphic image, localization, trivial ring extensions and amalgamation rings." @default.
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- W4220781380 date "2022-03-11" @default.
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- W4220781380 title "On 𝑆-weakly prime ideals of commutative rings" @default.
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- W4220781380 doi "https://doi.org/10.1515/gmj-2022-2141" @default.
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