Shahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401ON SPECTRA OF HERMITIAN RANDIĆ MATRIX OF SECOND KIND173196373110.22044/jas.2024.13993.1787ENABharaliDepartment of Mathematics
DIbrugarh University, IndiaBikashBhattacharjyaDepartment of Mathematics
Indian Institute of Technology GuwahatiSumantaBorahResearch Scholar
Dept of Mathematics
Dibrugarh UniversityIdweep JyotiGogoiResearch Scholar
Dept of Mathematics
Dibrugarh University0000-0001-5205-8915Journal Article20231223Let $X$ be a mixed graph and $\omega=\frac{1+\i \sqrt{3}}{2}$. We write $i\rightarrow j$, if there is an oriented edge from a vertex $v_i$ to another vertex $v_j$, and $i\sim j$ for an un-oriented edge between the vertices $v_i$ and $v_j$. The degree of a vertex $v_i$ is denoted by $d_i$. We propose the Hermitian Randi\'c matrix of second kind $R^\omega(X)\coloneqq(R^\omega_{ij})$, where $R^\omega_{ij}=\frac{1}{\sqrt{d_id_j}}$ if $i \sim j$, $R^\omega_{ij}= \frac{\omega}{\sqrt{d_id_j}}$ and $R^\omega_{ji}= \frac{\overline{\omega}}{\sqrt{d_id_j}}$ if $i\rightarrow j$, and 0 otherwise. In this paper, we investigate some spectral features of this novel Hermitian matrix and study a few properties like positiveness, bipartiteness, edge-interlacing etc. We also compute the characteristic polynomial for this new matrix and obtain some upper and lower bounds for the eigenvalues and the energy of this matrix.https://jas.shahroodut.ac.ir/article_3731_614a66ebf946b4987473e14e6558d278.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401COMMUTATIVITY FOR THE WEAKLY RIGHT CANCELLATIVE SEMIRINGS: AN ENTIRELY NOVEL CATEGORY OF SEMIRINGS AND A WEAK CONDITION FOR COMMUTATIVITY RESEARCH197208373210.22044/jas.2024.13745.1764ENKamal CharrabiCharrabiDepartment of Mathematics, Faculty of Sciences, Moulay Ismaïl University, P.O. Box 11201, Meknes, MoroccoAbdellahMamouniDepartment of Mathematics, Faculty of Sciences, Moulay Ismaïl University, P.O. Box 11201, Meknes, MoroccoBaderNejjarLaboratory of Innovant Technologies, High School of Technology, SMBA University, P.O. Box 2427, Fes, MoroccoJournal Article20231021The goal of this study is to provide an innovation for commutativity research that is less than the strong condition prime ring. This paper will describe weakly right cancellative semirings and examine how commutativity and generalized derivations apply to this class of semirings. A detailed explanation and classification of some of these generalized derivations are also included.https://jas.shahroodut.ac.ir/article_3732_7b260ccd1078584ca0a4b8f596376e64.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401LAPLACIAN SPECTRUM AND ENERGY OF NON-COMMUTING GRAPHS OF FINITE RINGS209244373310.22044/jas.2024.14111.1802ENMonalishaSharmaDepartment of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India.
Department of Mathematics, Baosi Banikanta Kakati College Nagaon, Barpeta, PIN - 781311, Assam, India.Rajat KantiNathDepartment of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India.Journal Article20240126We compute spectrum, energy, Laplacian spectrum/ energy and signless Laplacian spectrum/energy of non-commuting graphs of certain finite non-commutative rings. In particular, we consider finite rings $R$ such that $|R| = p^2, p^3, p^4$, $p^5$, $p^2q$ and $p^3q$, where $p$ and $q$ are primes. Further, we consider $n$-centralizer finite\\ rings for $n \, = \,4, \, 5$ \, and \, $p \,+ \,2$; \, more generally, finite rings with central quotients isomorphic to $\mathbb{Z}_p \times \mathbb{Z}_p$. Our computations reveal that non-commuting graphs of these rings are L-integral. We also determine whether non-commuting graphs of these rings are integral, Q-integral, hyperenergetic, L-hyperenergetic or Q-hyperenergetic.https://jas.shahroodut.ac.ir/article_3733_a0fa3cd589474451f4ae7f8a796ebaa3.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401INTUITIONISTIC FUZZY TRANSLATION AND MULTIPLICATION OF PMS-SUBALGEBRAS OF A PMS-ALGEBRA245262373410.22044/jas.2024.14102.1801ENBeza LamesginDersehDepartment of Mathematics, Debre Markos University, P.O. Box 79, Debre Markos, Ethiopia.0000-0002-7726-5248Journal Article20240126In this paper, we apply the concepts of intuitionistic fuzzy translations and intuitionistic fuzzy multiplications of intuitionistic fuzzy sets to the PMS-subalgebras of a PMS algebra and investigate several related results. The relationships between intuitionistic fuzzy PMS-subalgebras of a PMS-algebra and intuitionistic fuzzy ω-translations, and intuitionistic fuzzy ζ-multiplications of intuitionistic fuzzy PMS-subalgebras are discussed. Finally, we discuss the ideas of intuitionistic fuzzy magnified ζω - translations of intuitionistic fuzzy PMS-subalgebras of a PMS-algebra and investigate some associated results.https://jas.shahroodut.ac.ir/article_3734_37d4e7861fb8308204d366e9b15cc1db.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401ON THE COFINITENESS OF LOCAL COHOMOLOGY MODULES263269373510.22044/jas.2024.14393.1825ENGholamrezaPirmohammadiPayame Noor University
19395-3697 Tehran, Iran.Journal Article20240404Suppose that $\ab$ is an ideal of a given commutative Noetherian ring $R$ such that the $R$-modules $H^1_{\ab}(M)$ and $H^3_{\ab}(M)$ are $\ab$-cofinite, for every finitely generated $R$-modules $M$. In this paper, it is shown that the $R$-modules $H^i_{\ab}(M)$ are $\ab$-cofinite, for all finitely generated $R$-modules $M$ and all integers $i\in\Bbb{N}_0$.https://jas.shahroodut.ac.ir/article_3735_ccd634e8ae9473969244b323ddd34fd4.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401RAMANUJAN POLAR GRAPHS271280373610.22044/jas.2024.14231.1809ENValentinoSmaldoreDipartimento di Tecnica e Gestione dei Sistemi Industriali, Università degli Studi di Padova, Stradella S.
Nicola 3, 36100, Vicenza, Italy.0000-0003-3433-3164Journal Article20240224Recently, a construction of minimal codes arising from a family of almost Ramanujan graphs was shown. Ramanujan graphs are examples of expander graphs that minimize the second-largest eigenvalue of their adjacency matrix. We call such graphs Ramanujan, since all known non-trivial constructions imply the Ramanujan conjecture on arithmetical functions. In this paper, we prove that some families of tangent graphs of finite classical polar spaces satisfy Ramanujan's condition. If the polarity is unitary, or it is orthogonal and the quadric is over the binary field, the tangent graphs are strongly regular, and we know their spectrum. By direct computation, it is possible to show which families of tangent graphs are Ramanujan.https://jas.shahroodut.ac.ir/article_3736_4b4dac96d79fabe7c1de11412e72276f.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401CAPABILITY OF LOW-DIMENSIONAL NILPOTENT 3-LIE ALGEBRAS281295373710.22044/jas.2024.13818.1773ENHamidDarabiDepartment of Mathematics, Esfarayen University of Technology, Esfarayen, Iran.Journal Article20231110In this paper, we characterize the capability of nilpotent n- Lie algebras of dimension<br />at most n + 3 over an arbitrary field when n > 2$ and the capability of 7 -<br />dimensional nilpotent 3 -Lie algebras over field $\mathcal {K} $ with $char \mathcal {K}<br />\ ne 2$.https://jas.shahroodut.ac.ir/article_3737_8b7da69f5189e14a53731fa77bb251a0.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401K-bi-g-frames in Hilbert spaces297315373810.22044/jas.2024.14492.1834ENMohamedRossafiLaboratory Analysis, Geometry and Applications, Higher School of Education and Training, University Ibn
Tofail, Kenitra, Morocco.AbdelilahKararaLaboratory Analysis, Geometry and Applications, Department of Mathematics, University Ibn Tofail, Kenitra, Morocco.Journal Article20240506The notion of K-frames generalizes ordinary frames in that the lower frame bound applies only to elements within the range of K. This paper will introduce the new concept of K-bi-g-frames for Hilbert spaces. Then, we examine some characterizations with the help of a biframe operator. Finally, we investigate several results about the stability of K-bi-g-frames produced using frame theory methods.https://jas.shahroodut.ac.ir/article_3738_840512308b3e834d9c52e9cc1a1714ee.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401GENERALIZED LUCAS PRIMES IN THE FERMAT-EULER EQUATION317330373910.22044/jas.2024.14045.1790ENHayderHashimFaculty of Computer Science and Mathematics, University of Kufa, P.O. Box 21, 54001, Al Najaf, Iraq.Journal Article20240108The property of having infinitely many prime numbers award these numbers to have many applications in various fields of sciences. One of the most important applications is their use in the creation of many public key cryptosystems' private keys. Therefore, the main aim of this paper is considering a well known form of primes generated by the Fermat-Euler equation $p=x^2+dy^2$ and studying whether or not this form keeps the property of generating infinitely many primes if the unknowns $x$, $y$ and $p$ are terms in certain binary recurrence sequences called the Lucas sequences of the first kind $\{u_n(a,b)\}$ or the second kind $\{v_n(a,b)\}$. In other words, in this paper we present a technique for investigating the integer solutions $(x,y,p)$ of the equation $p=x^2+dy^2$, where the unknowns are terms in $\{u_n(a,b)\}$ or $\{v_n(a,b)\}$. We also apply this technique for determining the solutions $(x,y,p)=(t_i(a,b),t_j(a,b),t_k(a,b))$ with $1 \leq i \leq j \leq k$, where $t_n(a,b)$ represents the general term $u_n(a,b)$ or $v_n(a,b)$ under certain conditions on the integers $a$ and $b$.https://jas.shahroodut.ac.ir/article_3739_ce9198af9a72b319536578a9ab46fb3d.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401THE PARTITION DIMENSION AND $k$-DOMINATION NUMBER OF TWO SPECIFIC GRAPHS331342374010.22044/jas.2024.14317.1816ENAliZafariDepartment of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-4697, Tehran,
Iran.SaeidAlikhaniDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran.Journal Article20240315For an ordered $k$-partition $\Omega = \{S_1, S_2, ..., S_k\}$ of vertex set of a connected graph $G$ and a vertex $v$ of $G$, the representation of $v$ with respect to $\Omega$ is defined as the $k$-tuple $r(v |\Omega) = (d(v, S_1), d(v, S_2), ..., d(v, S_k )).$ The partition $\Omega$ is called a resolving partition of $G$, if $r(u|\Omega)\neq r(v|\Omega)$ <br />for all distinct $u, v \in V(G)$. The partition dimension of a graph $G$, denoted by $pd(G)$, is the cardinality of a minimum resolving partition of $G$. <br />A subset $D\subseteq V(G)$ is $k$-dominating in $G$, if every vertex of $V(G)\setminus D$ has at least $k$ neighbors in $D$. The minimum cardinality among all $k$-dominating sets is called the $k$-domination number of $G$, denoted by $\gamma_k(G)$. In this paper, we determine the partition dimension of cocktail party graph $CP(m+1)$ and corona product $G\circ\overline{K_m}$. Moreover, we obtain $k$-domination numbers for $CP(m+1)$ and corona product $C_n\circ\overline{K_m}$.https://jas.shahroodut.ac.ir/article_3740_af8a41a2bae4aeaf1816b1399a8df30d.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401CLASSIFICATION OF MONOIDS BY CONDITION (GPWPsec) OF RIGHT ACTS343367374110.22044/jas.2024.14066.1800ENMaliheShafieiDepartment of Mathematics, Sistan and Baluchestan University, P.O. Box 987-98155, Zahedan, Iran.HosseinMohammadzadeh SaanyDepartment of Mathematics, Sistan and Baluchestan University, P.O. Box 987-98155, Zahedan, Iran.ParisaRezaeiDepartment of Mathematics, Sistan and Baluchestan University, P.O. Box 987-98155, Zahedan, Iran.Journal Article20240124In (Categories and General Algebraic<br />Structures with Applications, 12(1):175-197 (2020)), Rashidi et al. introduced GPW-flatness<br />of acts over monoids as a generalization of principal<br />weak flatness.<br />In this paper, we introduce Condition (GPWPsec) of acts over<br />monoids and compare it with GPW-flatness. Also, we obtain<br />some general properties of Condition (GPWPsec) and characterize <br />those monoids for which this condition implies some other<br />properties and vice versa.<br /><br /><br />در( رسته ها و ساختارهای جبری عمومی با کاربردها 12(1):175-197(2020))، رشیدی و همکاران خاصیت<br />همواری - GPW<br />سیستم ها روی تکواره ها را به عنوان تعمیمی از به طور اساسی ضعیف همواری معرفی کردند. در این مقاله شرط <br />(〖GPWP〗_sec)<br />از سیستم ها روی تکواره ها را ارائه و آن را با <br />همواری - GPW<br />مقایسه می کنیم. همچنین برخی از خواص کلی شرط <br />(〖GPWP〗_sec)<br />. را به دست می آوریم و به دسته بندی تکوارهایی خواهیم پرداخت که این شرط سایر خواص را نتیجه دهد و برعکسhttps://jas.shahroodut.ac.ir/article_3741_8e9317df23f0bb184867fb0c671b7ea4.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814220260401t-PRIME SUBMODULES AND THEIR DECOMPOSITIONS369381374210.22044/jas.2024.14373.1822ENJavadMoghaderiDepartment of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran.AdnanTercanDepartment of Mathematics, Hacettepe University Beytepe Campus, Beytepe/ANKARA, Turkey.Journal Article20240328Let $R$ be a commutative ring with identity. For $t\in N$, a proper submodule $N$ of an $R$-module $M$ is called a t-prime submodule if $rm\in N~(r\in R, m\in M)$, then $m\in N$ or $r^t\in (N:_RM)$. We obtain some other characterizations of t-prime submodules. Also by some other notions like t-secondary submodules, various properties of t-prime submodules are investigated. To this end, we deal with irreducible as well as reduced t-prime decompositions of a submodule. We provide several examples with illustrate our results.https://jas.shahroodut.ac.ir/article_3742_83aeb62dca792b2e1b0978312d2a2581.pdf