Shahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901ŁUKASIEWICZ FUZZY FILTERS IN HOOPS120283210.22044/jas.2022.12139.1632ENMohammad Mohseni TakalloDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti
University, Tehran, Iran.Mona Aaly KologaniHatef Higher Education Institute, Zahedan, Iran.Young Bae JunDepartment of Mathematics Education, Gyeongsang National University, Jinju
52828, Korea.0000-0002-0181-8969Rajab Ali BorzooeiDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti
University, Tehran, Iran.0000-0001-7538-7885Journal Article20220722By applying the concept of the Lukasiewicz fuzzy set to the filter in hoops, the Lukasiewicz fuzzy filter is introduced and its properties are investigated.<br />The relationship between fuzzy filter and Lukasiewicz fuzzy filter is discussed.<br />Conditions for the Lukasiewicz fuzzy set to be a Lukasiewicz fuzzy filter are provided, and<br />characterizations of Lukasiewicz fuzzy filter are displayed.<br />The conditions under which the three subsets, $\in$-set, q-set, and O-set, will be filter are explored.https://jas.shahroodut.ac.ir/article_2832_98c4de79264b52334e140c21f2b08277.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901NEW FUNDAMENTAL RELATIONS IN HYPERRINGS AND THE CORRESPONDING QUOTIENT STRUCTURES2141283310.22044/jas.2022.10071.1501ENPeyman GhiasvandDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.Saeed MirvakiliDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.Bijan DavvazDepartment of Mathematical Sciences, Yazd University, Yazd, Iran.https://orcid.org/00Journal Article20200915In this article, we introduce and analyze the smallest equivalence binary relation $\chi ^{*}$ on a hyperring $R$ such that the quotient $R/\chi ^{*}$, the set of all equivalence classes, is a commutative ring with identity and of characteristic $m$. The characterizations of commutative rings with identity via strongly regular relations is investigated and some properties on the topic are presented. Moreover, we introduce a new strongly regular relation $\sigma^{*}_{p}$ such that the quotient structure is a $p$-ring. Moreover, we introduce a new strongly regular relation $\sigma^{*}_{p}$ such that the quotient structure is a $p$-ring.https://jas.shahroodut.ac.ir/article_2833_457f4c8b5ef1a32d867659bb3549f982.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901BORDERED GE-ALGEBRAS4358283410.22044/jas.2022.11184.1558ENRavikumar BandaruDepartment of Mathematics, GITAM(Deemed to be University), P.O. Box 502329,
Telangana State, India0000-0001-8661-7914Mehmet Ali OzturkDepartment of Mathematics, Faculty of Arts and Sciences, Adıyaman University,
P.O. Box 02040, Adıyaman, TurkeyYoung Bae JunDepartment of Mathematics Education, Gyeongsang National University, P.O. Box
52828, Jinju, Korea.0000-0002-0181-8969Journal Article20210908The notions of (transitive, commutative, antisymmetric) bordered GE-algebras are introduced,<br />and their properties are investigated. Relations between a commutative bordered GE-algebra and an<br />antisymmetric bordered GE-algebra are considered, and also relations between a commutative bordered<br />GE-algebra and a transitive bordered GE-algebra are discussed. Relations between a bordered GE-algebra and a bounded Hilbert algebra are stated, and the conditions under which every bordered GE-algebra (resp., bounded Hilbert algebra) can be a bounded Hilbert algebra (resp., bordered GE-algebra) are found. The concept of duplex bordered GE-algebras is introduced, and its properties are investigated. Relations between an antisymmetric bordered GE-algebra and a duplex bordered GE-algebra are discussed, and the conditions under which an antisymmetric bordered GE-algebra can be a duplex GE-algebra are established. A characterization of a duplex bordered GE-algebra is provided. A new bordered GE-algebra called cross bordered GE-algebra which is wider than duplex bordered GE-algebra is introduced, and its properties are investigated. Relations between a duplex bordered GE-algebra and a cross bordered GE-algebra are considered.https://jas.shahroodut.ac.ir/article_2834_d6c60e41844c3533f73a16ed6893470f.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901DERIVATIONS OF PRIME FILTER THEOREMS GENERATED BY VARIOUS $\cap $-STRUCTURES IN TRANSITIVE $GE$-ALGEBRAS5978283510.22044/jas.2022.11542.1583ENSambasiva RAO MukkamalaDepartment of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra
Pradesh, India.0000-0002-1627-9603Journal Article20220104Properties of prime filters and maximal filters of transitive GE-algebras are investigated. An element-wise characterization is derived for the smallest GE-filter containing a given set. It is proved that the set of all GE-filters of a transitive GE-algebra forms a complete distributive lattice. Four different versions of a prime filter theorem are generalized in transitive GE-algebras. A necessary and sufficient condition is derived for a proper filter of a commutative GE-algebra to become a prime filter.https://jas.shahroodut.ac.ir/article_2835_300aa20d6cfe0944e1e6b3a24cfd13f5.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901THE UNIT GRAPH OF A COMMUTATIVE SEMIRING7989283610.22044/jas.2022.11957.1612ENLaithun BoroDepartment of Mathematics, North-Eastern Hill University P.O. Box 793022,
Shillong, India.0000-0002-3852-1755Madan MohanSinghDepartment of Basic Sciences & Social Sciences, North-Eastern Hill University,
P.O. Box 793022, Shillong, India.0000-0002-1088-6832Jituparna GoswamiDepartment of Mathematics, Gauhati University, P.O. Box 781014, Guwahati,
India.0000-0002-1786-752XJournal Article20220531Let S be a commutative semiring with unity and U(S) be the set of all units of S. The unit graph of S, denoted by G(S), is the undirected graph with vertex set S and two distinct vertices x and y are adjacent if and only if x + y ∈ U(S). In this article, we have investigated some properties of unit graph G(S) of S regarding completeness, bipartiteness, connectedness, diameter and girth. Finally, we find a necessary and sufficient condition for G(S) to be traversable.https://jas.shahroodut.ac.ir/article_2836_cf33c9288a9bbc12414f964d9bc4eb79.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901$R$-CONVEX SUBSETS OF BIMODULES OVER $*$-RINGS91103283910.22044/jas.2022.11817.1605ENIsmail NikoufarDepartment of Mathematics, Payame Noor University, Tehran, Iran.nikoufar@yahoo.comAli Ebrahimi MeymandDepartment of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr
University of Rafsanjan, Rafsanjan, Iran.Journal Article20220412Let $M$ and $N$ be bimodules over the unital $*$-rings $R$ and $B$, respectively.<br />We investigate the notion of $R$-convexity and the corresponding notion of $R$-extreme points.<br />We discuss the effect of an $f$-homomorphism on<br />$R$-convex subsets and its\linebreak $R$-extreme points.<br />Namely, we declare how an $f$-homomorphism<br />from $M$ to $N$ carries $R$-convex subsets and its $R$-extreme points to $B$-convex subsets and its $B$-extreme points<br />and vice versa.\linebreak Moreover, we confirm that the $R$-convex hull of invariant subsets under $f$-homomorphisms<br />remains invariant.https://jas.shahroodut.ac.ir/article_2839_b650b30e1ebfa76f61e4df4d1d6331a3.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901n−ABSORBING I−PRIME HYPERIDEALS IN MULTIPLICATIVE HYPERRINGS105121284010.22044/jas.2022.12069.1621ENAli Abdullah MenaMathematics Department, Faculty of Science, Soran University, P.O. Box 44008,
Soran, Erbil Kurdistan Region, Iraq.Ismael AkrayMathematics Department, Faculty of Science, Soran University, P.O. Box 44008,
Soran, Erbil Kurdistan Region, Iraq.0000-0002-2166-4135Journal Article20220705In this paper, we define the concept $I-$prime hyperideal in a multiplicative hyperring $R$. A proper hyperideal $P$ of $R$ is an $I-$prime hyperideal if for $a, b \in R$ with $ab \subseteq P-IP$ implies $a \in P$ or $b \in P$. We provide some characterizations of $I-$prime hyperideals. Also we conceptualize and study the notions $2-$absorbing $I-$prime and $n-$absorbing $I-$prime hyperideals into multiplicative hyperrings as generalizations of prime ideals. A proper hyperideal $P$ of a hyperring $R$ is an $n-$absorbing $I-$prime hyperideal if for $x_1, \cdots,x_{n+1} \in R$ such that $x_1 \cdots x_{n+1} \subseteq P-IP$, then $x_1 \cdots x_{i-1} x_{i+1} \cdots x_{n+1} \subseteq P$ for some $i \in \{1, \cdots ,n+1\}$. We study some properties of such generalizations. We prove that if $P$ is an $I-$prime hyperideal of a hyperring $R$, then each of $\frac{P}{J}$, $S^{-1} P$, $f(P)$, $f^{-1}(P)$, $\sqrt{P}$ and $P[x]$ are $I-$prime hyperideals under suitable conditions and suitable hyperideal $I$, where $J$ is a hyperideal contains in $P$. Also, we characterize $I-$prime hyperideals in the decomposite hyperrings. Moreover, we show that the hyperring with finite number of maximal hyperideals in which every proper hyperideal is $n-$absorbing $I-$prime is a finite product of hyperfields.https://jas.shahroodut.ac.ir/article_2840_8f4d1faed84b37d6d78b9129a5bd11af.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901ON INVERSE LIMIT OF A PROJECTIVE SYSTEM OF BL-ALGEBRAS123133284110.22044/jas.2022.12222.1643ENReza Tayebi KhoramiDepartment of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.0000-0003-3291-722XJournal Article20220819In this paper, the inverse limits of a projective system of basic logic algebras (BL-algebras) are introduced, and their basic properties are studied. The set of congruences of a BL-algebra<br />is considered as a poset. Then, a quotient inverse system and a quotient inverse limit on it are constructed. Moreover, by setting filters of a BL-algebra, quotient projective and inverse systems are<br />constructed.https://jas.shahroodut.ac.ir/article_2841_08dcfa24d882ccd53f417575464cab96.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS135147284210.22044/jas.2022.12107.1629ENKoombail Shahul HameedDepartment of Mathematics, K M M Government Women’s College, Kannur, P.O.
Box 670004, Kerala, India0000-0003-0905-3865Kunhumbidukka Othayoth RamakrishnanDepartment of Mathematics, K M M Government Women’s College, Kannur, P.O.
Box 670004, Kerala, IndiaJournal Article20220713Given a matrix A with elements from a field of characteristic zero, the transin-<br />verse A# of A is defined as the transpose of the matrix obtained by replacing the <br />non-zero elements of A by their inverses and leaving zeros, if any, unchanged.<br />We discuss the properties of this matrix operation in some detail and as an important application, we reinvent the celebrated matrix tree theorem for gain graphs.<br />Characterization of balance in connected gain graphs using its Laplacian matrix becomes an immediate consequence.https://jas.shahroodut.ac.ir/article_2842_63f0c500dfc9cf0ede99189cacc5ba3a.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901NON-NILPOTENT GRAPH OF COMMUTATIVE RINGS149162284310.22044/jas.2023.12064.1620ENHussain Mohammed Imdadul HoqueDepartment of Mathematics, Gauhati University, Guwahati-781014, India.Helen KumariSaikiaDepartment of Mathematics, Gauhati University, Guwahati-781014, India.Jituparna GoswamiDepartment of Mathematics, Gauhati University, Guwahati-14, Assam, India.0000-0002-1786-752XDiksha PatwariDepartment of Mathematics, Gauhati University, Guwahati-781014, India.Journal Article20220704Let R be a commutative ring with unity. Let Nil(R) be the set of all nilpotent elements of R and Nil(R) = R \ Nil(R) be the set of all non-nilpotent elements of R. The non-nilpotent graph of R is a simple undirected graph GNN(R) with Nil(R) as vertex set and any two distinct vertices x and y are adjacent if and only if x+y ∈ Nil(R).<br />In this paper, we introduce and discuss the basic properties of the graph GNN(R). We also study the diameter and girth of GNN(R). Further, we determine the domination number and the bondage number of GNN(R). We establish a relation between diameter and domination number of GNN(R). We also establish a relation between girth and bondage number of GNN(R).https://jas.shahroodut.ac.ir/article_2843_3c09101e97af59b1db3801b6537792ce.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901ON (α; τ)-P-DERIVATIONS OF NEAR-RINGS163177284410.22044/jas.2023.12352.1661ENSamir MouhssineDepartment of Mathematics, University Sidi Mohammed Ben Abdellah-Fez,
Polydisciplinary Faculty-Taza, LSI, P.O. Box 1223, Taza, MoroccoAbdelkarim BouaDepartment of Mathematics, University Sidi Mohammed Ben Abdellah-Fez,
Polydisciplinary Faculty-Taza, LSI, P.O. Box 1223, Taza, Morocco.Journal Article20221020The relationship between derivations and algebraic structures of quotient near-rings has become a fascinating topic in modern algebra in recent decades. Assume $\mathcal{N}$ is a near-ring and $P$ is its prime ideal. In this paper we introduce the notion of $(\alpha, \tau )$-$P$-derivation in near-rings. Also, we study the structure of the quotient near-rings $N/P$ that satisfies certain algebraic identities involving $(\alpha, \tau )$-$P$-derivation.https://jas.shahroodut.ac.ir/article_2844_4e2cfe591ca4db7f536f074c85a303d0.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901DUAL RICKART (BEAR) MODULES AND PRERADICALS179191284510.22044/jas.2023.12207.1641ENSamira AsgariDepartment of Mathematics, Faculty of Mathematical Sciences, University of
Mazandaran, Babolsar, IranYahya TalebiDepartment of Mathematics, Faculty of Mathematical Sciences, University of
Mazandaran, Babolsar, IranAli Reza Moniri HamzekolaeeDepartment of Mathematics, Faculty of Mathematical Sciences, University of
Mazandaran, Babolsar, Iran.0000-0002-2852-7870Journal Article20220811In this work, we introduce dual Rickart (Baer) modules via the con-<br />cept of preradicals. It is shown that W is -d Rickart if and only if<br />W = (W) L such that (W) is a dual Rickart module. We prove<br />that a module W is -d Baer if and only if W is -d Rickart and W<br />satises strongly summand sum property for d.s. submodules of W<br />contained in (W). Via (RR), we characterize right -d Baer rings.https://jas.shahroodut.ac.ir/article_2845_7c4afd23f0c6acdcc3837b13f82d208e.pdf