Direct product of B-algebras

Lingcong, Jacel Angeline V.; Endam, Joemar C.

doi:10.12988/ija.2016.51278

Cited by 9 publications

(15 citation statements)

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“…In this paper, we have introduced the concept of the direct product of infinite family of B -algebras, we call the external direct product, which is a generalization of the direct product in the sense of Lingcong and Endam [12]. We proved that the external direct product of B -algebras is also a B -algebra.…”

Section: Discussionmentioning

confidence: 99%

“…Then, they extended the concept of the direct product of B -algebra to finite family B -algebra, and some of the related properties were investigated as follows: Definition 6. [12] Let (P i ; * i ) be an algebra for each i ∈ {1, 2, ..., k}. Define the direct product of algebras P 1 , P 2 , ..., P k to be the structure ( k i=1 P i ; ⊗), where…”

Section: External Direct Product Of B-algebrasmentioning

confidence: 99%

“…Then, direct product groups are applied to other algebraic structures. In 2016, Lingcong and Endam [12] discussed the notion of the direct product of B -algebras, 0-commutative B -algebras, and B -homomorphisms and obtained related properties, one of which is a direct product of two B -algebras, which is also a B -algebra. Then, they extended the concept of the direct product of B -algebra to finite family B -algebra, and some of the related properties were investigated.…”

Section: Introductionmentioning

confidence: 99%

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Direct Product of Infinite Family of B-Algebras

Chanmanee

Chinram

Prasertpong

et al. 2022

Eur. J. Pure Appl. Math.

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The concept of the direct product of finite family of B-algebras is introduced by Lingcong and Endam [J. A. V. Lingcong and J. C. Endam, Direct product of B-algebras, Int. J. Algebra,10(1):33-40, 2016.]. In this paper, we introduce the concept of the direct product of infinite family of B-algebras, we call the external direct product, which is a generalization of the direct product in the sense of Lingcong and Endam. Also, we introduce the concept of the weak direct product of B-algebras. Finally, we provide several fundamental theorems of (anti-)B-homomorphisms in view of the external direct product B-algebras.

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Section: Discussionmentioning

confidence: 99%

Section: External Direct Product Of B-algebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Direct Product of Infinite Family of B-Algebras

Chanmanee

Chinram

Prasertpong

et al. 2022

Eur. J. Pure Appl. Math.

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“…Then, direct product groups are applied to other algebraic structures. In 2016, Lingcong and Endam [25] discussed the notion of the direct product of B-algebras, 0-commutative Balgebras, and B-homomorphisms and obtained related properties, one of which is a direct product of two B-algebras, which is also a B-algebra. Then, they extended the concept of the direct product of B-algebra to finite family B-algebra, and some of the related properties were investigated.…”

Section: Introductionmentioning

confidence: 99%

External and weak direct products of UP (BCC)-algebras

Chanmanee¹,

Chinram²,

Phrommarat³

et al. 2022

J. Math. Computer Sci.

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“…The notion of direct product was firstly studied in group and some of their generalizations were obtained, such as the direct product of the group is a group and the direct product of the abelian group is again an abelian group are the ones that can be given as properties that are obtained in these studies. In 2016, the notion of direct product of B-algebra, 0commutative B-algebra and B-homomorphism were studied by Lingcong and Endham [18]. In 2020, the concept of direct product of BP-algebras was given by Setani, Gemawati and Deswita [19].…”

Section: Introductionmentioning

confidence: 99%