Crossing cubic Lie algebras

Anas Al-Masarwah; Nadeen Kdaisat; Majdoleen Abuqamar; Kholood Alsager; Anas Al-Masarwah; Nadeen Kdaisat; Majdoleen Abuqamar; Kholood Alsager

doi:10.3934/math.20241075

AIMS Mathematics

2024, Volume 9, Issue 8: 22112-22129. doi: 10.3934/math.20241075

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Research article

Crossing cubic Lie algebras

1.
Department of Mathematics, Faculty of Science, Ajloun National University, P. O. Box 43, Ajloun 26810, Jordan; anas.almasarwah@anu.edu.jo
2.
Department of Mathematics, Yarmouk University, Shafiq Irshidat Street, Irbid 21163, Jordan; nadeengdesat1@gmail.com
3.
Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan; mjabuqamar@gmail.com
4.
Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia

Received: 19 March 2024 Revised: 02 July 2024 Accepted: 08 July 2024 Published: 16 July 2024
MSC : 06F35, 03G25, 03B52, 03B05

An interval-valued fuzziness structure is an effective approach addressing ambiguity and for expressing people's hesitation in everyday situations. An $ \mathcal{N} $-structure is a novel technique for solving practical problems. This is beneficial for resolving a variety of issues, and a lot of progress is being made right now. In order to develop crossing cubic structures ($ \mathcal{CCS}s $), Jun et al. amalgamate interval-valued fuzziness and $ \mathcal{N} $-structures. In this manuscript, our main contribution is to originate the concepts of crossing cubic ($ \mathcal{CC} $) Lie algebra, $ \mathcal{CC} $ Lie sub-algebra, ideal, and homomorphism. We investigate some properties of these concepts. In a Lie algebra, the construction of a quotient Lie algebra via the $ \mathcal{CC} $ Lie ideal is provided. Furthermore, the $ \mathcal{CC} $ isomorphism theorems are presented.
- Lie algebras,
- crossing cubic Lie algebras,
- crossing cubic fields,
- crossing cubic solvable Lie algebras,
- crossing cubic nilpotent Lie algebras,
- fuzzy logic
Citation: Anas Al-Masarwah, Nadeen Kdaisat, Majdoleen Abuqamar, Kholood Alsager. Crossing cubic Lie algebras[J]. AIMS Mathematics, 2024, 9(8): 22112-22129. doi: 10.3934/math.20241075

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Abstract

An interval-valued fuzziness structure is an effective approach addressing ambiguity and for expressing people's hesitation in everyday situations. An $ \mathcal{N} $-structure is a novel technique for solving practical problems. This is beneficial for resolving a variety of issues, and a lot of progress is being made right now. In order to develop crossing cubic structures ($ \mathcal{CCS}s $), Jun et al. amalgamate interval-valued fuzziness and $ \mathcal{N} $-structures. In this manuscript, our main contribution is to originate the concepts of crossing cubic ($ \mathcal{CC} $) Lie algebra, $ \mathcal{CC} $ Lie sub-algebra, ideal, and homomorphism. We investigate some properties of these concepts. In a Lie algebra, the construction of a quotient Lie algebra via the $ \mathcal{CC} $ Lie ideal is provided. Furthermore, the $ \mathcal{CC} $ isomorphism theorems are presented.

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