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Symmetry
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Symmetry in Algebra and Its Applications
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Symmetry in Algebra and Its Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 7585

Special Issue Editors

Dr. Mohammad Abobala

E-Mail Website
Guest Editor
Department of Mathematics, Tishreen University, Latakia, Syrian Arab Republic
Interests: group theory; algebraic structures
Prof. Dr. Arsham Borumand Saeid

E-Mail Website
Guest Editor
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Interests: algebraic structures; algebraic logic; fuzzy sets and applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Algebraic structures are concerned with studying operations between objects, and this has become a very useful tool in pure mathematics and applied sciences such as physics, cryptography, and biology. Algebra and number theory are working together to open new doors through these fields.

The main goal of this Special Issue is to create a collection of novel and influential results in the fields of algebraic structures and number theory, as well as their applications in many related fields.

A new perspective will be obtained for applied sciences and natural sciences.

In this Special Issue, research articles that contribute to the literature will be included by focusing on findings and applications containing algebraic structures and number theory. We invite all interested researchers to contribute to this Special Issue with original and review articles that contain new motivating ideas and trends.

Potential topics include but are not limited to:

  • Group Theory;
  • Rings and ideals;
  • Modules and projections;
  • Vector spaces;
  • Matrix theory and related problems;
  • Number theory and diophantine equations;
  • Neutrosophic algebra;
  • Fuzzy algebraic structures;
  • Algebraic games;
  • Dual numbers;
  • Split complex numbers;
  • Lattice theory and symmetric elements;
  • Graph theory;
  • N cyclic algebraic structures;
  • Algebraic cryptography;
  • Symmetry to algebraic functions;
  • Algebraic topology and geometry.

Dr. Mohammad Abobala
Prof. Dr. Arsham Borumand Saeid
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • algebraic structures matrices diophantine equations
  • rings
  • neutro algebras
  • fuzzy algebras
  • vector spaces
  • linear functions

Published Papers (6 papers)

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Research

11 pages, 264 KiB  
Article
Saturated Varieties of Semigroups
by Muneer Nabi, Amal S. Alali and Sakeena Bano
Symmetry 2023, 15(8), 1612; https://doi.org/10.3390/sym15081612 - 21 Aug 2023
Viewed by 827
Abstract
The complete characterization of saturated varieties of semigroups remains an unsolved problem. The primary objective of this paper is to make significant progress in this direction. We initially demonstrate that the variety of semigroups defined by the identity [...] Read more.
The complete characterization of saturated varieties of semigroups remains an unsolved problem. The primary objective of this paper is to make significant progress in this direction. We initially demonstrate that the variety of semigroups defined by the identity axy=ayxa is saturated. The next main result establishes that the variety of semigroups determined by the identity axy=ayax is saturated. Finally, we show that medial semigroups satisfying the identity xy=xyn, where n≥2, are also saturated. These results collectively lead to the conclusion that epis from these saturated varieties are onto. This paper thus offers substantial progress towards the comprehensive characterization of saturated varieties of semigroups. Full article
(This article belongs to the Special Issue Symmetry in Algebra and Its Applications)
10 pages, 263 KiB  
Article
Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings
by Ahmed Hatip
Symmetry 2023, 15(8), 1588; https://doi.org/10.3390/sym15081588 - 15 Aug 2023
Viewed by 1129
Abstract
Symbolic n-plithogenic algebraic structures are considered as symmetric generalizations of classical algebraic structures because they have n + 1 symmetric components. This paper is dedicated to generalizing symbolic 3-plithogenic rings by defining symbolic 4-plithogenic rings and 5-plithogenic rings; these new classes of n-symbolic [...] Read more.
Symbolic n-plithogenic algebraic structures are considered as symmetric generalizations of classical algebraic structures because they have n + 1 symmetric components. This paper is dedicated to generalizing symbolic 3-plithogenic rings by defining symbolic 4-plithogenic rings and 5-plithogenic rings; these new classes of n-symbolic plithogenic algebraic structures will be defined for the first time, and their algebraic substructures will be studied. AH structures are considered to be a sign of the presence of symmetry within these types of ring, as they consist of several parts that are similar in structure and symmetrical, and when combined with each other, they have a broader structure resembling the classical consonant structure. Many related substructures will be presented such as 4-plithogenic/5-plithogenic AH-ideals, 4-plithogenic/5-plithogenic AH-homomorphisms, and 4-plithogenic AHS-isomorphisms will be discussed. We will show our results in terms of theorems, with many clear numerical examples that explain the novelty of this work. Full article
(This article belongs to the Special Issue Symmetry in Algebra and Its Applications)
14 pages, 265 KiB  
Article
On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices
by Hamiyet Merkepçi
Symmetry 2023, 15(8), 1494; https://doi.org/10.3390/sym15081494 - 27 Jul 2023
Cited by 4 | Viewed by 566
Abstract
Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These [...] Read more.
Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. In this research, we will find easy-to-use algorithms for calculating the determinant of a symbolic 3-plithogenic/4-plithogenic matrix, and for finding its inverse based on its classical components, and even for diagonalizing matrices of these types. On the other hand, we will present a new algorithm for calculating the eigenvalues and eigenvectors associated with matrices of these types. Also, the exponent of symbolic 3-plithogenic and 4-plithogenic real matrices will be presented, with many examples to clarify the novelty of this work. Full article
(This article belongs to the Special Issue Symmetry in Algebra and Its Applications)
16 pages, 5744 KiB  
Article
A Complete Breakdown of Politics Coverage Using the Concept of Domination and Double Domination in Picture Fuzzy Graph
by Rashad Ismail, Sami Ullah Khan, Samer Al Ghour, Esmail Hassan Abdullatif Al-Sabri, Maha Mohammed Saeed Mohammed, Shoukat Hussain, Fiaz Hussain, Giorgio Nordo and Arif Mehmood
Symmetry 2023, 15(5), 1044; https://doi.org/10.3390/sym15051044 - 08 May 2023
Cited by 2 | Viewed by 1364
Abstract
The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in [...] Read more.
The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzification (anti-symmetric) methods depends on the specific application and the type of fuzzy sets being used, whether they are symmetric or anti-symmetric. There are various methods for each process, such as centroid, max-min, and weighted average methods for defuzzification. Finally, in the last section, drawing from the application example, the features and benefits of PFGs with respect to fuzzy graphs and intuitionistic fuzzy graphs are compared and discussed. Full article
(This article belongs to the Special Issue Symmetry in Algebra and Its Applications)
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21 pages, 345 KiB  
Article
2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings
by Serkan Onar, Kostaq Hila, Sina Etemad, Ali Akgül, Manuel De la Sen and Shahram Rezapour
Symmetry 2023, 15(3), 740; https://doi.org/10.3390/sym15030740 - 17 Mar 2023
Viewed by 1466
Abstract
The aim of this study is to provide a generalization of prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing vague weakly complete Γ-ideals of commutative Γ-rings. A novel algebraic structure of a primary vague Γ-ideal of a [...] Read more.
The aim of this study is to provide a generalization of prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing vague weakly complete Γ-ideals of commutative Γ-rings. A novel algebraic structure of a primary vague Γ-ideal of a commutative Γ-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Γ-ideals of Γ-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Γ-ideals and 2-absorbing Γ-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Γ-ideal of a Γ-ring and 2-absorbing K-vague Γ-ideal of a Γ-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Γ-ring of R induced by a 2-absorbing vague weakly complete Γ-ideal of a 2-absorbing Γ-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Γ-ideal. Full article
(This article belongs to the Special Issue Symmetry in Algebra and Its Applications)
24 pages, 2924 KiB  
Article
Prediction Model of a Generative Adversarial Network Using the Concept of Complex Picture Fuzzy Soft Information
by Sami Ullah Khan, Esmail Hassan Abdullatif Al-Sabri, Rashad Ismail, Maha Mohammed Saeed Mohammed, Shoukat Hussain and Arif Mehmood
Symmetry 2023, 15(3), 577; https://doi.org/10.3390/sym15030577 - 22 Feb 2023
Cited by 6 | Viewed by 1212
Abstract
A computer vision model known as a generative adversarial network (GAN) creates all the visuals, including images, movies, and sounds. One of the most well-known subfields of deep learning and machine learning is generative adversarial networks. It is employed for text-to-image translations, as [...] Read more.
A computer vision model known as a generative adversarial network (GAN) creates all the visuals, including images, movies, and sounds. One of the most well-known subfields of deep learning and machine learning is generative adversarial networks. It is employed for text-to-image translations, as well as image-to-image and conceptual image-to-image translations. Different techniques are used in the processing and generation of visual data, which can lead to confusion and uncertainty. With this in mind, we define some solid mathematical concepts to model and solve the aforementioned problem. Complex picture fuzzy soft relations are defined in this study by taking the Cartesian product of two complex picture fuzzy soft sets. Furthermore, the types of complex picture fuzzy soft relations are explained, and their results are also discussed. The complex picture fuzzy soft relation has an extensive structure comprising membership, abstinence, and non-membership degrees with multidimensional variables. Therefore, this paper provides modeling methodologies based on complex picture fuzzy soft relations, which are used for the analysis of generative adversarial networks. In the process, the score functions are also formulated. Finally, a comparative analysis of existing techniques was performed to show the validity of the proposed work. Full article
(This article belongs to the Special Issue Symmetry in Algebra and Its Applications)
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