Some properties of 2-absorbing primary ideals in lattices

Wasadikar, Meenakshi; Gaikwad, Karuna T.

doi:10.1016/j.akcej.2018.01.015

AKCE International Journal of Graphs and Combinatorics

2019

DOI: 10.1016/j.akcej.2018.01.015

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Some properties of 2-absorbing primary ideals in lattices

Meenakshi Wasadikar

Karuna T. Gaikwad

Abstract: We introduce the concepts of a primary and a 2-absorbing primary ideal and the radical of an ideal in a lattice. We study some properties of these ideals. A characterization for the radical of an ideal to be a primary ideal is given. Also a characterization for an ideal I to be a 2-absorbing primary ideal is proved. Examples and counter examples are given wherever necessary. c

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2024

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Cited by 2 publications

References 5 publications

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Some New Results on S-prime Ideals of a Finite Commutative Ring as S-meet Semilattice

Duraisamy,

Varadharajan

2024

ACM

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Let ℜ be the finite commutative ring with unity and Is be the S-prime ideal of a ring ℜ. The set Ls forms a partially ordered set (poset) by the subset relation. Initially, the interplay of the semilattice theoretic properties of a poset with the ring theoretic properties are studied with suitable examples. The number of maximal chain of a poset is compared with the number of prime ideals of a ring. It is proved that every maximal element of a poset is the prime ideal of a ring. A prime order ring is shown as a lattice. If the order of the ring is the product of two primes, then the trivial ideal is expressed as the meet of every pair of a poset. Further, the cardinality of the poset is determined in terms of the divisors of the order of the ring . A new meet-semilattice called the S-meet semilattice (Ls, ⋀, ⊆) is defined and the generalized Hasse diagrams of the S-meet semilattice of a ring of prime powers, product of prime powers are drawn in this paper in order to find the properties of S-meet semilattice. Finally, the ideals, the prime ideals and the maximal ideals of the S-meet semilattice are described in terms of the down-sets of S-meet semilattice where the results are listed with an example at the end.

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Some New Results on S-prime Ideals of a Finite Commutative Ring as S-meet Semilattice

Duraisamy,

Varadharajan

2024

ACM

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On 2-Absorbing Strong Primary Fuzzy Ideals in Lattices

Sujitha,

Dheena,

Sivakumar

2024

Missouri J. Math. Sci.

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Some properties of 2-absorbing primary ideals in lattices

Cited by 2 publications

References 5 publications

Some New Results on S-prime Ideals of a Finite Commutative Ring as S-meet Semilattice

Some New Results on S-prime Ideals of a Finite Commutative Ring as S-meet Semilattice

On 2-Absorbing Strong Primary Fuzzy Ideals in Lattices

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