Residuation Properties and Weakly Primary Elements in Lattice Modules

Manjarekar, C. S.; Kandale, Ujwala Narahari

doi:10.1155/2014/858323

Cited by 3 publications

(2 citation statements)

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“…al. in [19] and [20] A multiplicative lattice L is a complete lattice provided with commutative, associative and join distributive multiplication in which the largest element 1 acts as a multiplicative identity. An element e ∈ L is called meet principal if a ∧ be = ((a : e) ∧ b)e for all a, b ∈ L.…”

Section: Introductionmentioning

confidence: 99%

Ï†-Prime and Ï†-Primary Elements in Lattice Modules

Bingi

Manjarekar²

2021

Eur. J. Pure Appl. Math.

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In this paper, we introduce φ-prime and φ-primary elements in an L-module M. Many of its characterizations and properties are obtained. By counter examples, it is shown that a φ-prime element of M need not be prime, a φ-primary element of M need not be φ-prime, a φ-primary element of M need not be prime and a φ-primary element of M need not be primary. Finally, some results for almost prime and almost primary elements of an L-module M with their characterizations are obtained. Also, we introduce the notions of n-potent prime (respectively n-potent primary) elements in L and M to obtain interrelations among them where n≥2.

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Section: Introductionmentioning

confidence: 99%

Ï†-Prime and Ï†-Primary Elements in Lattice Modules

Bingi

Manjarekar²

2021

Eur. J. Pure Appl. Math.

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“…If each element of M is a join of principal .compact/ elements of M; then M is called a principally generated lattice module, briefly PG lattice module .compactly generated lattice, briefly CG lattice module/. For various information on lattice module, one is referred to [6][7][8].…”

Section: Introductionmentioning

confidence: 99%