Shahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101NEW MAJORIZATION FOR BOUNDED LINEAR OPERATORS IN HILBERT SPACES112272710.22044/jas.2022.11318.1564ENFarzaneh GorjizadehDepartment of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord,
Iran.Noha EftekhariDepartment of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord,
Iran.Journal Article20211021This work aims to introduce and investigate a preordering in $B(\mathcal{H}),$ <br />the Banach space of all bounded linear operators defined on a complex <br />Hilbert space $\mathcal{H}.$ It is called strong majorization and denoted by $S\prec_{s}T,$ for <br />$S,T\in B(\mathcal{H}).$ The strong majorization follows majorization defined by Barnes, but not vice versa. <br />If $S\prec_{s}T,$ then $S$ inherits some properties of $T.$ <br /> The strong majorization will be extended for the d-tuple of operators in $B(\mathcal{H})^{d}$ and <br />is called joint strong majorization denoted by $S\prec_{js}T,$ for $S,T\in B(\mathcal{H})^{d}.$ We show that <br />some properties of strong majorization are satisfied for joint strong majorization.https://jas.shahroodut.ac.ir/article_2727_112aa1ae252de4ef66eff1917dd0dc89.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101ISOTONIC CLOSURE FUNCTIONS ON A LOCALE1332272810.22044/jas.2022.12101.1627ENToktam HaghdadiDepartment of Basic Sciences, Birjand University of Technology, P.O. Box 226,
Birjand, Iran.0000-0002-3003-5250Ali Akbar EstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.
Box 397, Sabzevar, Iran.0000-0001-8993-5109Journal Article20220712In this paper, we introduce and study isotonic closure functions on a locale. These are pairs of the form $(L, \underline{{\mathrm{cl}}}_L)$, where<br />$L$ is a locale and $\underline{{\mathrm{cl}}}_L\colon \mathcal{S}\!\ell(L) \rightarrow \mathcal{S}\!\ell(L)$<br />is an isotonic closure function on the sublocales of $L$. Moreover, we introduce generalized<br />$\underline{{\mathrm{cl}}}_L$- closed sublocales in isotonic closure locales and discuss some of their properties. Also, we introduce and study the category $ \textbf{ICF} $ whose objects and morphisms are isotonic closure functions $(L, \underline{{\mathrm{cl}}}_L)$ and localic maps, respectively.https://jas.shahroodut.ac.ir/article_2728_9048642dc8c7868e1956de9b20810e1e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101ABSORBING PRIME MULTIPLICATION MODULES OVER A PULLBACK RING3351272910.22044/jas.2022.11638.1593ENFarkhondeh FarzalipourDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.0000-0003-2494-5466Peyman GhiasvandDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.Journal Article20220206The main purpose of this article is to present a new approach to the classification of all indecomposable absorbing prime multiplication modules with finite-dimensional top over pullback rings of two Dedekind domains. First, we give a complete description of the absorbing prime multiplication modules over a local Dedekind domain. In fact, we extend the definition and results given in \cite{108} to a more general absorbing prime multiplication modules case. Next, we establish a connection between the absorbing prime multiplication modules and the pure-injective modules over such rings.https://jas.shahroodut.ac.ir/article_2729_023ba765031d3b4ae873cbaa59711efd.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101A KIND OF GRAPH STRUCTURE ASSOCIATED WITH ZERO-DIVISORS OF MONOID RINGS5363273010.22044/jas.2022.12238.1646ENMohammad EtezadiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Tabriz, Tabriz, Iran.Abdollah AlhevazFaculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box
316-3619995161, Shahrood, Iran0000-0001-6167-607XJournal Article20220828Let $R$ be an associative ring and $M$ be a monoid. In this paper, we introduce new kind of graph structure asociated with zero-divisors of monoid ring $R[M]$, calling it the $M$-Armendariz graph of a ring $R$ and denoted by $A(R,M)$. It is an undirected graph whose vertices are all non-zero zero-divisors of the monoid ring $R[M]$ and two distinct vertices $\alpha=a_{1}g_{1}+\cdots+ a_{n}g_{n}$ and $\beta=b_{1}h_{1}+\cdots+b_{m}h_{m}$ are adjacent if and only if $a_{i}b_{j}=0$ or $b_{j}a_{i}=0$ for all $i,j$. We investigate some graph properties of $A(R,M)$ such as diameter, girth, domination number and planarity. Also, we get some relations between diameters of the $M$-Armendariz graph $A(R,M)$ and that of zero divisor graph $\Gamma(R[M])$, where $R$ is a reversible ring and $M$ is a unique product monoid.https://jas.shahroodut.ac.ir/article_2730_aa5f7f98a22a1436fed3a41607d47007.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101QUOTIENT STRUCTURES IN EQUALITY ALGEBRAS6582273110.22044/jas.2022.11919.1608ENRajab Ali BorzooeiDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti
University, Tehran, Iran.0000-0001-7538-7885Mohammad 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, P.O. Box
52828, Jinju, Korea.0000-0002-0181-8969Journal Article20220514The notion of fuzzy ideal in bounded equality algebras is defined, and several properties are studied. Fuzzy ideal generated by a fuzzy set is established, and a fuzzy ideal is made by using the collection of ideals. Characterizations of fuzzy ideal are discussed. Conditions for a fuzzy ideal to attains its infimum on all ideals are provided. Homomorphic image and preimage of fuzzy ideal are considered. Finally, quotient structures of equality algebra induced by (fuzzy) ideal are studied.https://jas.shahroodut.ac.ir/article_2731_816b89436b2d69ab6d7e4651e726983b.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101A CLASSIFICATION OF EXTENSIONS GENERATED BY A ROOT OF AN EISENSTEIN-DUMAS POLYNOMIAL8391273210.22044/jas.2022.11808.1603ENَAzadeh NiksereshtDepartment of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.0000-0002-3892-9881Journal Article20220407It is known that for a discrete valuation v of a field K with value group Z, an valued extension field (K′, v′) of (K, v) is generated by a root of an Eisenstein polynomial with respect to v having coefficients in K if and only if the extension (K′, v′)/(K, v) is totally ramified. The aim of this paper is to present the analogue of this result for valued field extensions generated by a root of an Eisenstein-Dumas polynomial with respect to a more general valuation (which is not necessarily discrete). This leads to classify such algebraic extensions of valued fields.https://jas.shahroodut.ac.ir/article_2732_348fbdd2888fbfecbecd8c5bf762901d.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101SOME PROPERTIES OF SUPER-GRAPH OF (G (R))^c AND ITS LINE GRAPH93112273310.22044/jas.2022.12098.1628ENKrishna LalitkumarPurohitDepartment of Applied Sciences, RK University, P.O. Box 360003, Rajkot, India.Jaydeep HarjibhaiParejiyaDepartment of Mathematics, Government Polytechnic, P.O. Box 360003, Rajkot,
India.Journal Article20220716Let R be a commutative ring with identity 1≠0. The comaximal ideal graph of R is the simple, undirected graph whose vertex set is the set of all proper ideals of the ring R not contained in Jacobson radical of R and two vertices I and J are adjacent in this graph if and only if I+J=R. In this article, we have discussed the graph G(R) whose vertex set is the set of all proper ideals of ring R and two vertices I and J are adjacent in this graph if and only if I+J≠R. In this article, we have discussed some interesting results about G(R) and its line graph.https://jas.shahroodut.ac.ir/article_2733_0d8a6563070e57797521e004c7b8cd4c.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101EXTENSION AND TORSION FUNCTORS WITH RESPECT TO SERRE CLASSES113123273410.22044/jas.2022.11683.1597ENSajad ArdaDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.Seadat Ollah FaramarziDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.Journal Article20220220In this paper we generalize the Rigidity Theorem and Zero Divisor Conjecture for an arbitrary Serre subcategory of modules. For this purpose, for any regular<br />M-sequence x1; :::; xn with respect to S we prove that if TorR 2 ((x1;:::;x R n); M) 2 S, then<br />TorR i ((x1;:::;x R n); M) 2 S, for all i ≥ 1. Also we show that if Extn R+2((x1;:::;x R n); M) 2 S,<br />then Exti R((x1;:::;x R n); M) 2 S, for all integers i ≥ 0 (i ̸= n).https://jas.shahroodut.ac.ir/article_2734_a44138a7e8e87779437d5827a091c18b.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101UNIFORMLY N-IDEALS OF COMMUTATIVE RINGS125136273510.22044/jas.2022.12319.1658ENMohammad BaziarDepartment of Mathematics, Yasouj University, P.O. Box 75914, Yasouj, Iran.Afroozeh JafariDepartment of Mathematics, Yasouj University, P.O. Box 75914, Yasouj, Iran.Ece YYetkin CelikelDepartment of Electrical Electronics Engineering, Faculty of Engineering,
Hasan Kalyoncu University, Gaziantep, TurkeyJournal Article20221004In this paper, we introduce the concept of uniformly $n$-ideal of<br />commutative rings which is a special type of $n$-ideal. We call a<br />proper ideal $I$ of $R$ a uniformly $n$-ideal if there exists a<br />positive integer $k$ for $a,b\in R$ whenever $ab\in I$ and<br />$a\notin I$ implies that $b^{k}=0.$ The basic properties of<br />uniformly $n$-ideals are investigated in detail. Moreover, some<br />characterizations of uniformly $n$-ideals are obtained for some<br />special rings.https://jas.shahroodut.ac.ir/article_2735_07b171e74ee0c25f5d9a0f0e3b03fa6e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101ON THE MINIMAXNESS AND ARTINIANNESS DIMENSIONS137145273610.22044/jas.2022.11553.1584ENJafar AzamiDepartment of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.Mohammad Reza DoustimehrDepartment of Mathematics, University of Tabriz, Tabriz, Iran;
and School of Mathematics, Institute for research in fundamental sciences (IPM),
P.O. Box 19395-5746, Tehran, Iran.Journal Article20220105Let R be a commutative Noetherian ring, I, J be ideals of R such that<br />J ⊆ I, and M be a finitely generated R-module. In this paper, we prove that the<br />invariants AJI<br />(M) := inf{i ∈ N0 | JtHi<br />I (M) is not Artinian for all t ∈ N0} and inf{i ∈<br />N0 | JtHi<br />I (M) is not minimax for all t ∈ N0} are equal. In particular, we show that the<br />invariants AII<br />(M) and inf{i ∈ N0 | Hi<br />I (M) is not minimax} are equal. We also establish<br />the local-global principle, AJI<br />(M) = inf{AJRp<br />IRp<br />(Mp)|p ∈ Spec (R)}, in some cases.https://jas.shahroodut.ac.ir/article_2736_4b4c99809b6ebd6a8e31a4d4f121ee1e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101POLYMATROIDAL IDEALS AND LINEAR RESOLUTION147153273710.22044/jas.2022.11950.1610ENSomayeh BandariDepartment of Mathematics, Buein Zahra Technical University, Buein Zahra,
Qazvin, Iran.0000-0002-2975-3183Journal Article20220527Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and<br />$I\subset S$ be a monomial ideal with a linear<br />resolution. Let<br />$\frak{m}=(x_1,\ldots,x_n)$ be the unique homogeneous maximal ideal and $I\frak{m}$ be a<br />polymatroidal ideal. We prove that if either $I\frak{m}$ is polymatroidal with strong<br />exchange property, or $I$ is a monomial ideal in at most 4<br />variables, then $I$ is polymatroidal. We also show that the first<br />homological shift ideal of polymatroidal ideal is again<br />polymatroidal.https://jas.shahroodut.ac.ir/article_2737_32a69698369215d4849edb4b52ec0186.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101ON THE DOMINATION NUMBER OF THE SUM ANNIHILATING IDEAL GRAPH OF A COMMUTATIVE RING AND ON THE DOMINATION NUMBER OF ITS COMPLEMENT155177273810.22044/jas.2022.12110.1630ENSubramanian VisweswaranDepartment of Mathematics, Saurashtra University, P.O. Box 360005, Rajkot,
India.Patat SarmanDepartment of Mathematics, Government Polytechnic, P.O. Box 362263,
Junagadh, India.
.Journal Article20220714The rings considered in this article are commutative with identity which are not integral domains. Let R be a ring. The sum annihilating ideal graph of R is an undirected graph whose vertex set is the set of all non-zero annihilating ideals of R and distinct vertices I and J are adjacent if and only if their sum is an annihilating ideal. The aim of this article is to discuss some results on the domination number of the sum annihilating ideal graph of R and on the domination number of its complement.https://jas.shahroodut.ac.ir/article_2738_355b94442aa9f4d4a286220dcbd7759f.pdf