Pylonsupport

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We investigate the localization and the S 2 prime avoidance lemma in commutative rings

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We introduce the concept of S 2 primary ideal which is a generalization of 2 primary ideal Let P be a proper ideal of R disjoint with S We say that P is an S 2 primary ideal

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Weakly 2 prime ideals in commutative rings Let R be a commutative ring with identity and S b a multi plicative subset of R with 1 S A proper ideal Q of R with Q S is called a weakly S 2 prime

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This paper aims to characterize S 2 prime ideals which serve as a generalization encompassing both 2 prime ideals and S prime ideals To accomplish this objective we construct an ideal which distinct

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We investigate the localization and the S 2 prime avoidance lemma in commutative rings Furthermore we explore the properties of this class of ideals in trivial ring extensions and amalgamated algebras

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Next assuming the Axiom of Choice it is proved that if R is a commutative ring and T is a commutative R algebra which is generated by a set I then each chain of prime ideals of T lying over the same

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We explore properties of S 2 absorbing ideals and their connections to S prime ideals as well as their behavior in various ring constructions Additionally we define the S 2 absorbing radical of an ideal

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The document introduces the concept of S prime ideals in commutative rings S prime ideals generalize prime ideals and enjoy analogous properties The paper studies properties of S

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Recent attention on weakly 2 prime and S 2 prime ideals This study aims for new characterizations of weakly S 2 prime ideals a generalizatio that includes both weakly 2 prime and S 2 prime ideals To