Shahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601ON ZAGREB ENERGIES OF SOME GRAPH OPERATIONS383406381810.22044/jas.2024.14103.1799ENIdweep JyotiGogoiDepartment of Mathematics, Dibrugarh University, Assam, India.0000-0001-5205-8915SumantaBorahDepartment of Mathematics, Dibrugarh University, Assam, India.AnkurBharaliDepartment of Mathematics, Dibrugarh University, Assam, India.Journal Article20240124Recently, Zagreb energies, a graph invariant based on the eigenvalues of the Zagreb matrices have been proposed as an analogous to graph energy. In this communication, the Zagreb energies and Zagreb spectral radius are examined in relation to a number of graph operations, such as m-splitting graphs, m-shadow graphs, m-duplicate graphs, and extended bipartite double graphs. Further, we explore these generalised graphs within the context of specific graph types such as complete graphs, complete bipartite graphs, cycle graphs, and the complements of cycle graphs. Furthermore, we report an error present in [19] that contradicts the claim of hyperenergetic behaviour for the splitting graph of regular graphs, and also establish the non-hyperenergetic behaviour of the m-shadow graph.https://jas.shahroodut.ac.ir/article_3818_a1d6835786a8015a5827f77ecbea8a4b.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601NON-PARALLEL KRULL DIMENSION OF MODULES407425381910.22044/jas.2024.14545.1841ENNasrinShiraliDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.MohammadMaschizadehDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20240518In this paper, the concept of non-parallel Krull (resp., Noetherian) dimension of an $ R $-module are introduced and some related properties are investigated. Using these concepts, we generalize some of the results of our previous work and sometimes obtain new results about np-Artinian (resp., np-Noetherian) modules. We give a characterization for modules with non-parallel Krull (resp., Noetherian) dimension and show that these modules have finite type dimension. It is shown that any $ R $-module $ M $ with non-parallel Krull dimension at most $ \alpha $ is either atomic or $ \lambda $-f.e. for some $ \lambda\leq\alpha $. <br />Also, it is proved that any np-Noetherian $R$-module has non-parallel Krull dimension.<br />In particular, for semiprime right non-atomic rings, we show that Krull dimension and non-parallel Krull dimension coincide.https://jas.shahroodut.ac.ir/article_3819_bfedd4fb2ca0ef29f5dddb68835a21b0.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601VERTEX DECOMPOSABILITY AND WEAKLY POLYMATROIDAL IDEALS427438382010.22044/jas.2024.14707.1854ENAmirMafiDepartment of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran.DlerNaderiDepartment of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran.HeroHeroSaremiDepartment of Mathematics, Sa.C., Islamic Azad University, Sanandaj, Iran.Journal Article20240623Let $K$ be a field and $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$. Let $\Delta$ be a simplicial complex on $n$ vertices and $I=I_{\Delta}$ be its Stanley-Reisner ideal.<br />In this paper, we show that if $I$ is a matroidal ideal then the following conditions are equivalent: $(i)$ $\Delta$ is sequentially Cohen-Macaulay; $(ii)$ $\Delta$ is shellable; $(iii)$ $\Delta$ is vertex decomposable. Also, if $I$ is a minimally generated by $u_1,\ldots,u_s$ such that $s\leq 3$ or $\supp(u_i)\cup\supp(u_j)=\{x_1,\ldots,x_n\}$ for all $i\neq j$, then $\Delta$ is vertex decomposable. Furthermore, we prove that<br />if $I$ is a monomial ideal of degree $2$ then $I$ is weakly polymatroidal if and only if $I$ has linear quotients if and only if $I$ is vertex splittable.https://jas.shahroodut.ac.ir/article_3820_b6c502776ab04f365619fe0d0cb3ed57.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601SOME ASPECTS OF K-HYPERIDEALS OF TERNARY HYPERSEMIRINGS439454382110.22044/jas.2024.14092.1798ENMd Salim MasudMollaDepartment of Mathematics, Barasat Govt. College, P.O. Box 700124, Barasat, India.Journal Article20240121This paper introduces the concept of k-hyperideals of ternary hypersemirings and explores some of its fundamental characteristics. Next, k-hyperideals are used to characterize prime ternary hypersemirings and ternary hypersemifields. Moreover, k-hyperideals explain the quotient of ternary hypersemirings. Finally, the new kind of ternary hypersemirings is formed using regular equivalence relations, and the set of all k-hyperideals is generated from them.https://jas.shahroodut.ac.ir/article_3821_19c3d47184d69ab2d625f72fe460c4ec.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601SOME RESULTS ON SUBRINGS OF $C(X)$ AND $C(X, \mathbb{C})$455463382210.22044/jas.2024.14897.1875ENLongjaijaiKharkamniDepartment of Mathematics, North Eastern Hill University, P.O. Box 793022, Meghalaya, India.SanghitaDuttaDepartment of Mathematics, North Eastern Hill University, P.O. Box 793022, Meghalaya, India.Journal Article20240807Let $X$ be a Tychonoff space and $\mathcal{R}[X]$ be the collection of all subrings of $C(X)$ that separate points and contain the identity element 1. In this paper, we establish a correspondence between ideals in $A(X)$ $\in$ $\mathcal{R}[X]$ and $z^{\gamma}_A$-filters on the completion of $X$ with respect to a uniform structure arising from the functions in $A(X)$. We also explore some properties of $z$-ideals, $z_A$-ideals and maximal ideals in these types of subrings of $C(X)$. For each subset $A(X)$ of $C(X)$, let $[A(X)]_c$ $=$ $\{f + ig: f, g \in A(X)\}$. We demonstrate that $[A(X)]_c$ is a $c$-type subring of $C(X, \mathbb{C})$ when $A(X)$ $\in$ $\mathcal{R}[X]$ is a $c$-type subring of $C(X)$. Finally, for an intermediate subring $A(X)$ of $C(X)$, we show that the completion of $X$ with respect to a suitable uniform structure derived from $[A(X)]_c$ is equal to $\upsilon_AX$, the $A$-compactification of $X$.https://jas.shahroodut.ac.ir/article_3822_f570affa91ac4410ab048aa6af0782b1.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601GENERALIZED SHERMAN-MORRISON-WOODBURY FORMULA FOR THE G-DRAZIN INVERSE465475382310.22044/jas.2025.14515.1836ENAliGhaffariDepartment of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.MarjanSheibani AbdolyousefiFarzanegan Campus, Semnan University, Semnan, Iran.FatemehZamiriDepartment of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.Journal Article20240511In this paper, we present generaized Sherman-<br />Morrison-Woodbury formula for the g-Drazin inverse in a Banach<br />algebra. New results for the g-Drazin invertibility of a<br />modified element a -cdb with the generalized Schur complement<br />dd - badc are given. The g-Drazin invertibility of a operator<br />matrix with nonsingular generalized Schur complement<br />under weaker restrictions is thereby establishedhttps://jas.shahroodut.ac.ir/article_3823_dd2e1bbee1fceda8286f23bdf53f9418.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601TORSION MAXIMAL SUBGROUPS OF GLn(D)477488382410.22044/jas.2025.14465.1831ENRezaFallah-MoghaddamDepartment of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.Journal Article20240426Let D be a division ring over its center F. Let<br />GLn(D)<br />be the general linear group over D. In this article we prove that<br />if<br />GLn(D)<br />contains a maximal torsion subgroup M then D = F,<br />Fp<br />charF = p > 0 and F is algebraic over its prime sub eld<br />when-<br />ever one of the following conditions occurs: (1) D is algebraic over<br />F; (2) there exists an element a<br />2<br />M such that<br />CMn(D)(F[a])<br />is<br />algebraic over F.https://jas.shahroodut.ac.ir/article_3824_2344112b1982103da7a4c45984968a14.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601ON THE SPECTRA OF TENSOR JOIN OF HYPERGRAPHS489508382910.22044/jas.2025.14919.1880ENVishnupriyaRamkumarDepartment of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram–624
302, Tamil Nadu, India.RajkumarRajendranDepartment of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram–624
302, Tamil Nadu, India.Journal Article20240809In this paper, we consider certain classes of hypergraphs constructed from the tensor join of hypergraphs, specifically the tensor join of hypergraphs constrained by vertex subsets and the $(H, \mathcal{T}_{\mathcal{S}})$-join of hypergraphs constrained by $\mathcal{S}$. We determine some eigenvalues of the adjacency tensor of these classes of hypergraphs by establishing corresponding eigenvectors. We demonstrate that the eigenvalues of the adjacency tensor of the constituting hypergraphs are also eigenvalues of the adjacency tensor of the join of a set of hypergraphs. Furthermore, as a special case of our results, we provide some eigenvalues and eigenvectors of the adjacency tensor for the join of non-uniform hypergraphs on a backbone hypergraph $H$ (and, similarly, for the join of $m$-uniform hypergraphs on a backbone hypergraph $H$). Additionally, we establish a relationship between the eigenvalues of the adjacency tensor of a hypergraph $H$ and certain eigenvalues of the adjacency tensor of the $(H, \mathcal{T}_{\mathcal{S}})$-join of hypergraphs constrained by $\mathcal{S}$. Using this relationship, we determine some eigenvalues and their corresponding eigenvectors for the adjacency tensor of the lexicographic product of two hypergraphs.https://jas.shahroodut.ac.ir/article_3829_2f5badf8e43df6dcb8fdeb21c46e7cb8.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601SOME REMARKS ON WEAKLY S-LASKERIAN MODULES509529383010.22044/jas.2025.14472.1832ENSubramanianVisweswaranDepartment of Mathematics, Saurashtra University, P.O. Box 360005, Rajkot, India.Journal Article20240429The rings considered in this paper are commutative with identity and the modules considered are modules over commutative rings and are unitary. We use R to denote a ring, S to denote a multiplicatively closed subset of R, and M to denote a module over R. We say that M is an S-Laskerian (respectively, a strongly S-Laskerian) R-module if M is an S-finite R-module and for any submodule N of M, either (N: M) meets S or there exist t in S and an S-decomposable (respectively, a strongly S-decomposable) submodule K of M such that tN is a submodule of K and K is contained in N. We say that M is a weakly S-Laskerian (respectively, weakly strongly S-Laskerian) R-module if each S-finite proper submodule of M is an S-Laskerian (respectively, a strongly Laskerian ) R-module. In this paper, we discuss some results on basic properties of weaklly S-Laskerian modules and we extend some of the properties of S-Laskerian modules to weakly S-Laskerian modules.https://jas.shahroodut.ac.ir/article_3830_a91e5ba4ea7f239d75e52f0446746a34.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601A GENERALIZATION OF SEMINOETHERIAN RINGS AND MODULES531547383110.22044/jas.2025.14717.1855ENMaryamDavoudianDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University
of Ahvaz, Ahvaz, Iran.0000-0003-3433-2444NahidNaseriDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University
of Ahvaz, Ahvaz, Iran.Journal Article20240627We study those modules in which all submodules contain a nonzero submodule with Noetherian dimension less than or equal to $\alpha $ where $\alpha $ is the least ordinal number with this property, calling them modules that have enough $\alpha$-noetherians. Also, we study those modules in which any nonzero factor module contains a nonzero submodule with Noetherian dimension less than or equal to $\alpha$, where $\alpha$ is the least ordinal number with this property, calling them $\alpha$-seminoetherians. Our work extends the results of Kourki and Tribak in Commu. Algebra (2022).https://jas.shahroodut.ac.ir/article_3831_7ea43323e763e6403a5d294e0dff437d.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601R-ideals of Almost Distributive Lattices549567383210.22044/jas.2025.14770.1865ENNoorbashaRafiDepartment of Mathematics, Siddhartha Academy of Higher Education, Deemed to be University,
Vijayawada, Andhra Pradesh, India-520 007.Natnael TAmareDepartment of Mathematics, University of Gondar, Gondar, Ethiopia.BalaiahMothukuriDepartment of Science and Humanities, Vasireddy Venkatadri International Technological University,
Guntur, Andhra Pradesh, India-522 508.
Email: balaiah_m19@hotmail.comTanniru SrinivasaRaoDepartment of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 101.Journal Article20240711The concepts have been introduced in Almost Distributive<br />Lattices(ADLs), namely, R-ideals and -ideals. A set of<br />conditions has been identified that are equivalent to converting an<br />E-ideal into an R-ideal. Moreover, it has been derived that for<br />any E-ideal, there exists a homomorphism with a dual dense kernel,<br />which is itself an R-ideal. The characterization of -ideals in<br />terms of R-ideals and congruences has been established. Additionally,<br />equivalent conditions have been established to demonstrate<br />that the space of all prime -ideals forms a Hausdorff space.https://jas.shahroodut.ac.ir/article_3832_16772292a8421246fabef89ca4afc7b6.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512814320260601THE BANASCHEWSKI-SIOEN NUCLEUS ON AN ALGEBRAIC FRAME569602383310.22044/jas.2025.15685.1927ENSiphamandlaBLOSEDepartment of Mathematical Sciences, University of South Africa, P.O. Box 392, Pretoria, South Africa.ThembaDubeDepartment of Mathematical Sciences, University of South Africa, P.O. Box 392, Pretoria, South Africa.Journal Article20250205In their construction of the Stone-\v{C}ech compactification using only ring ideals (as opposed to $\ell$-ideals), Banaschewski and Sioen define a certain nucleus on the coherent frame $\Rid(A)$ of radical ideals of a commutative ring $A$. In this paper we extend this nucleus to any algebraic frame that has a dense compact element and in which the meet of two compact elements is compact. Of course, not every such algebraic frame is coherent, so the extension is indeed a genuine extension. We then study some properties of this nucleus which are not considered by Banaschewski and Sioen.https://jas.shahroodut.ac.ir/article_3833_89e244085a5d559ff3d678963d3dcbf1.pdf