Special Issue "General Algebraic Structures"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 November 2019.

Special Issue Editors

Prof. Dr. Hee Sik Kim
E-Mail Website
Guest Editor
Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul 04763, Korea
Interests: BCK-algebras and its generalizations; Posets; Groupoid Theory; Semirings; Fuzzy algebras; Fibonacci numbers
Prof. Dr. Wiesław A. Dudek
E-Mail Website
Guest Editor
Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
Interests: Quasigroups; BCK-algebras; Fuzzy algebras
Prof. Dr. Arsham Borumand Saeid
E-Mail
Guest Editor
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Prof. Dr. Rajab Borzooei
E-Mail
Guest Editor
Department of Mathematics, Shahid Beheshti University, Tehran 1983963113, Iran
Prof. Dr. Xiaohong Zhang
E-Mail
Guest Editor
Department of Mathematics, Shaanxi University of Science and Technology, Xi’an 710021, China
Special Issues and Collections in MDPI journals
Prof. Dr. Jianming Zhan
E-Mail
Guest Editor
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China

Special Issue Information

Dear Colleagues,

R. H. Bruck's famous book, A Survey of Binary Systems, mainly discussed loops and semigroups. It is necessary to organize several groupoids dealing with various axioms. The area of “general algebraic structures” contains several groupoids, i.e., sets with a single binary operation satisfying some conditions. The well-known topics, e.g., groups, semigroups, monoids, BCK/BCI-algebra, etc., are not included in this area. It contains lots of generalized algebraic structures of these well-known mathematical structures simply by deleting/weakening/changing the axioms.

The notion of BCK/BCI-algebra was introduced by K. Iséki in 1965, alongside its generalizations, e.g., BCH-algebra, BH-algebra, BZ-algebra, BCC-algebra, pre-BCK-algebra and near-BCK-algebra. The notion of d-algebra was introduced by deleting two complicated axioms from BCK-algebra. After that, many algebraic structures appeared, e.g., B-, BE-, BF-, BG-, BM-, BN-, BO-, BP-, C-, CI-, Q, QS-algebra. Other important algebraic structures are implicative algebra, positive implication algebra, selective groupoids, pogroupoids, weak-zero groupoids, etc. These algebras have some inter-relationships with each other, and have more rooms for further research.

This Special Issue of Mathematics (MDPI) will provide an opportunity to construct an area of general algebraic structures, and will encourage researchers to publish their investigations in this area.

We will consider any paper in the area of general algebraic structures for possible publication. We will exclude papers on well-known algebras, e.g., groups, rings, fields, semigroups, lattices and posets, BCK/BCI-algebra, fuzzy algebraic theory, etc.

Prof. Dr. Hee Sik Kim
Prof. Dr. Wiesław A. Dudek
Prof. Dr. Arsham Borumand Saeid
Prof. Dr. Rajab Borzooei
Prof. Dr. Xiaohong Zhang
Prof. Dr. Jianming Zhan
Guest Editors

Manuscript Submission Information

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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. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

  • general algebraic structures
  • sets with a single binary operations (groupoids)
  • generalized groups
  • implicative algebra
  • generalized BCK/BCI-algebra

Published Papers (5 papers)

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Research

Open AccessArticle
Extending Structures for Lie 2-Algebras
Mathematics 2019, 7(6), 556; https://doi.org/10.3390/math7060556 - 18 Jun 2019
Abstract
The extending structures problem for strict Lie 2-algebras is studied. To provide the theoretical answer to this problem, this paper introduces the unified product of a given strict Lie 2-algebra g and 2-vector space V. The unified product includes some interesting products [...] Read more.
The extending structures problem for strict Lie 2-algebras is studied. To provide the theoretical answer to this problem, this paper introduces the unified product of a given strict Lie 2-algebra g and 2-vector space V. The unified product includes some interesting products such as semi-direct product, crossed product, and bicrossed product. The paper focuses on crossed and bicrossed products, which give the answer to the extension problem and factorization problem, respectively. Full article
(This article belongs to the Special Issue General Algebraic Structures)
Open AccessArticle
Graphs Based on Hoop Algebras
Mathematics 2019, 7(4), 362; https://doi.org/10.3390/math7040362 - 21 Apr 2019
Abstract
In this paper, we investigate the graph structures on hoop algebras. First, by using the quasi-filters and r-prime (one-prime) filters, we construct an implicative graph and show that it is connected and under which conditions it is a star or tree. By using [...] Read more.
In this paper, we investigate the graph structures on hoop algebras. First, by using the quasi-filters and r-prime (one-prime) filters, we construct an implicative graph and show that it is connected and under which conditions it is a star or tree. By using zero divisor elements, we construct a productive graph and prove that it is connected and both complete and a tree under some conditions. Full article
(This article belongs to the Special Issue General Algebraic Structures)
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Open AccessArticle
On Pre-Commutative Algebras
Mathematics 2019, 7(4), 336; https://doi.org/10.3390/math7040336 - 08 Apr 2019
Cited by 1
Abstract
In this paper, we introduce the notions of generalized commutative laws in algebras, and investigate their relations by using Smarandache disjointness. Moreover, we show that every pre-commutative B C K -algebra is bounded. Full article
(This article belongs to the Special Issue General Algebraic Structures)
Open AccessArticle
The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-(l, l)-Loops
Mathematics 2019, 7(3), 268; https://doi.org/10.3390/math7030268 - 15 Mar 2019
Cited by 10
Abstract
In this paper, some new properties of Abel Grassmann‘s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied. The following important results were proved: (1) an AG-NET-Loop is weakly commutative if, and only if, it is a commutative neutrosophic extended triplet (NETG); (2) every [...] Read more.
In this paper, some new properties of Abel Grassmann‘s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied. The following important results were proved: (1) an AG-NET-Loop is weakly commutative if, and only if, it is a commutative neutrosophic extended triplet (NETG); (2) every AG-NET-Loop is the disjoint union of its maximal subgroups. At the same time, the new notion of Abel Grassmann’s (l, l)-Loop (AG-(l, l)-Loop), which is the Abel-Grassmann’s groupoid with the local left identity and local left inverse, were introduced. The strong AG-(l, l)-Loops were systematically analyzed, and the following decomposition theorem was proved: every strong AG-(l, l)-Loop is the disjoint union of its maximal sub-AG-groups. Full article
(This article belongs to the Special Issue General Algebraic Structures)
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Open AccessFeature PaperArticle
Some Special Elements and Pseudo Inverse Functions in Groupoids
Mathematics 2019, 7(2), 173; https://doi.org/10.3390/math7020173 - 14 Feb 2019
Abstract
In this paper, we consider a theory of elements u of a groupoid ( X , ) that are associated with certain functions u ^ : X X , pseudo-inverse functions, which are generalizations of the inverses associated with units of [...] Read more.
In this paper, we consider a theory of elements u of a groupoid ( X , ) that are associated with certain functions u ^ : X X , pseudo-inverse functions, which are generalizations of the inverses associated with units of groupoids with identity elements. If classifying the elements u as special of one of twelve types, then it is possible to do a rather detailed analysis of certain cases, leftoids, rightoids and linear groupoids included, which demonstrates that it is possible to develop a successful theory and that a good deal of information has already been obtained with much more possible in the future. Full article
(This article belongs to the Special Issue General Algebraic Structures)
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