Hybrid ideals in semigroups

Anis, Saima; Khan, Madad; Jun, Young Bae

doi:10.1080/23311835.2017.1352117

Cited by 26 publications

(16 citation statements)

References 4 publications

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“…ey also introduced the concepts of hybrid linear space, hybrid subalgebra, and hybrid field. Moreover, hybrid structure applications have been studied in semigroups (see [22][23][24][25] and references there in), and recently, hybrid ideals of BCK � BCI-algebras were studied in [26][27][28][29]. For more important terminologies, the readers are referred to [30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Structures Applied to Subalgebras of BCH-Algebras

Muhiuddin

Al-Kadi

Khan

et al. 2021

Security and Communication Networks

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The algebraic structures have many applications in coding theory, cryptography, and security networks. In this paper, the notion of hybrid subalgebras of BCH -algebras is introduced and related properties are investigated. Moreover, some characterizations of hybrid subalgebras of BCH -algebras are given. Furthermore, we state and prove some theorems in hybrid subalgebras of BCH -algebras. The homomorphic images and inverse images of fuzzy BCH -subalgebras are studied and discussed.

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Section: Introductionmentioning

confidence: 99%

Hybrid Structures Applied to Subalgebras of BCH-Algebras

Muhiuddin

Al-Kadi

Khan

et al. 2021

Security and Communication Networks

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“…Using this notion, they introduce the concepts of a hybrid sub-algebra, a hybrid field and a hybrid linear space. Recently, the notion of hybrid structure and its applications to BCI-algebras and semigroups have been studied in (see [8,12,13,25] and references there in). Also, more concepts related to our study in different aspect have been studied in [2-6, 15, 22, 32, 33].…”

Section: Introductionmentioning

confidence: 99%

Ideal theory of BCK/BCI-algebras based on hybrid structures

Muhiuddin¹,

Al-Kadi²,

Mahboob³

2020

J. Math. Computer Sci.

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In this paper, the concept of hybrid ideals in BCK/BCI-algebras is introduced, and related properties are investigated. Further, it is proved that every hybrid ideal is hybrid sub-algebra in BCK/BCI-algebras, but the converse is not valid in general, and an example is provided in this regard. Some characterizations of hybrid ideals in BCK/BCI-algebras are given. Moreover, the notion of hybrid closed ideals in BCI-algebras is introduced, and some associated properties are studied. Furthermore, the hybrid intersection and hybrid union are also discussed.

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“…e idea of a hybrid subalgebra, a hybrid field, and a hybrid linear space was introduced with this notion. e hybrid structure theory and its applications to (BCK/BCI)-algebras and semigroups have recently been studied in (see [36][37][38][39][40] and references). e objective of this paper is to introduce the notions of hybrid p-ideal, hybrid h-ideal, and hybrid a-ideal in (BCI)-algebras and investigate their related properties.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Structures Applied to Ideals in BCI-Algebras

Muhiuddin

Al-Kadi

Mahboob³

2020

Journal of Mathematics

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In this paper, the notion of hybrid structure is applied to the ideal theory in BCI-algebras. In fact, we introduce the notions of hybrid p -ideal, hybrid h-ideal, and hybrid a-ideal in BCI-algebras and investigate their related properties. Furthermore, we show that every hybrid p -ideal (or h-ideal or a-ideal) is a hybrid ideal in a BCI-algebra but converse need not be true in general and in support, and we exhibit counter examples for each case. Moreover, we consider characterizations of hybrid p -ideal, hybrid h-ideal, and hybrid a-ideal in BCI-algebras.

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Hybrid ideals in semigroups

Cited by 26 publications

References 4 publications

Hybrid Structures Applied to Subalgebras of BCH-Algebras

Hybrid Structures Applied to Subalgebras of BCH-Algebras

Ideal theory of BCK/BCI-algebras based on hybrid structures

Hybrid Structures Applied to Ideals in BCI-Algebras

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