Primeness of Relative Annihilators in BCK-Algebra

Bordbar, Hashem; Muhiuddin, G.; Alanazi, Abdulaziz M.

doi:10.3390/sym12020286

Cited by 8 publications

(6 citation statements)

References 18 publications

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“…One of the motivations could be what happens for a decomposable ideal of a BCK-algebra under the homomorphism, or the associated prime ideals of a decomposable ideal under homomorphism. For more information about decompsable ideals and closure operations, please refer to [7].…”

Section: Discussionmentioning

confidence: 99%

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Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

2020

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We introduce the notions of meet, semi-prime, and prime weak closure operations. Using homomorphism of BCK-algebras φ : X → Y , we show that every epimorphic image of a non-zeromeet element is also non-zeromeet and, for mapping c l Y : I ( Y ) → I ( Y ) , we define a map c l Y ← on I ( X ) by A ↦ φ − 1 ( φ ( A ) c l Y ) . We prove that, if “ c l Y ” is a weak closure operation (respectively, semi-prime and meet) on I ( Y ) , then so is “ c l Y ← ” on I ( X ) . In addition, for mapping c l X : I ( X ) → I ( X ) , we define a map c l X → on I ( Y ) as follows: B ↦ φ ( φ − 1 ( B ) c l X ) . We show that, if “ c l X ” is a weak closure operation (respectively, semi-prime and meet) on I ( X ) , then so is “ c l X → ” on I ( Y ) .

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Section: Discussionmentioning

confidence: 99%

“…Besides, the notions of commutative, implicative, and positive implicative weak closure operations were investigated by [1]. Moreover, using the notation of weak closure operation, some algebraic structures have been defined and related properties investigated [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

2020

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“…Whatis the meaning of height of these types of ideals? For information about the maximality, primeness and height of ideals, please refer to [1,2,6,5].…”

Section: Discussionmentioning

confidence: 99%

A General Model of Neutrosophic Ideals in BCK/BCI-algebras Based on Neutrosophic Points

et al. 2020

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More general form of (∈, ∈ ∨q)-neutrosophic ideal is introduced, and their properties are investigated. Relations between (∈, ∈)-neutrosophic ideal and (∈, ∈ ∨q(kT ,kI ,kF ))-neutrosophic ideal are discussed. Characterizations of (∈, ∈∨q(kT ,kI,kF ))-neutrosophic ideal are discussed, and conditions for a neutrosophic set to be an (∈, ∈∨q(kT ,kI ,kF ))-neutrosophic ideal are displayed.

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“…A BCK/BCI-algebra is an important class of logical algebras introduced by K. Iséki (see [5,6]) and was extensively investigated by several researchers. Please refer to [7][8][9][10][11][12][13] We recall the definitions and basic results required in this paper. See the books [14,15] for further information regarding BCK/BCIalgebras.…”

Section: Preliminariesmentioning

confidence: 99%

Interior BCK/BCI-Algebras

Ahn¹,

Bordbar²,

Jun³

2021

IJCIS

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The notions of interior BCK/BCI-algebras, positive implicative interior BCK-algebras, (weak) interior ideals, positive implicative interior ideals, a positive implicative weak interior ideal of type 1, type 2, and type 3 are introduced, and related properties are investigated. A mapping is provided to the set of all involutions of a bounded BCK-algebra in relation to any interior BCKalgebra so that the set of all involutions of a bounded BCK-algebra can be an interior BCK-algebra. The relationship between interior ideals, weak interior ideals, and positive implicative interior ideals is established. The conditions under which a weak interior ideal can change to an interior ideal are founded. The conditions for an interior ideal to be a positive implicative interior ideal are provided. The scalability for a positive implicative interior ideal is discussed. The relationship between type 1, type 2, and type 3 on positive implicative weak interior ideals are investigated. The relationship between weak interior ideal and positive implicative weak interior ideal of type 1, type 2, and type 3 are established.

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Primeness of Relative Annihilators in BCK-Algebra

Cited by 8 publications

References 18 publications

Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

A General Model of Neutrosophic Ideals in BCK/BCI-algebras Based on Neutrosophic Points

Interior BCK/BCI-Algebras

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