Shahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901A SURVEY ON THE FUSIBLE PROPERTY OF SKEW PBW EXTENSIONS129231910.22044/jas.2021.10351.1513ENS.HigueraDepartment of Mathematics, Faculty of Science, Universidad Nacional de Colombia
- Sede Bogotá, Bogotá, D. C., Colombia.A.ReyesDepartment of Mathematics, Faculty of Science, Universidad Nacional de Colombia
- Sede Bogotá, Bogotá, D. C., Colombia.0000-0002-5774-0822Journal Article20201219We present several results that establish the fusible and the regular left fusible properties of the family of noncommutative rings known as skew Poincar'e-Birkhoff-Witt extensions. Our treatment is based on the recent works of Ghashghaei and McGovern [13], and Kosan and Matczuk [31] concerning the left fusibleness and the regular left fusibleness of skew polynomial rings of automorphism type. Since the results formulated in this paper can be applied to algebraic structures more general than skew polynomial rings, our contribution to the theory of fusibleness is to cover more families of rings of interest in branches as quantum groups, noncommutative algebraic geometry and noncommutative differential geometry. We provide illustrative examples of the ideas developed here.https://jas.shahroodut.ac.ir/article_2319_c2aef58091314d96afdcdaa00114bd72.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901VOLUNTARY GE-FILTERS AND FURTHER RESULTS OF GE-FILTERS IN GE-ALGEBRAS3147232010.22044/jas.2021.10357.1511ENA.Borumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid
Bahonar University of Kerman, P.O. Box 76169-14111, Kerman, Iran.0000-0001-9495-6027A.RezaeiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.0000-0002-6003-3993R.BandaruDepartment of Mathematics, GITAM(Deemed to be University), P.O. Box 502329
Telangana State, India.0000-0001-8661-7914Y. B.JunDepartment of Mathematics Education, Gyeongsang National University, P.O. Box
52828, Jinju, Korea.0000-0002-0181-8969Journal Article20201209Further properties on (belligerent) GE-filters are discussed, and the quotient GEalgebra via a GE-filter is established. Conditions for the set →<br />c to be a belligerent GE-filter<br />are provided. The extension property of belligerent GE-filter is composed. The notions of a<br />balanced element, a balanced GE-filter, an antisymmetric GE-algebra and a voluntary GE-filter<br />are introduced, and its properties are examined. The relationship between a GE-subalgebra<br />and a GE-filter is established. Conditions for every element in a GE-algebra to be a balanced<br />element are provided. The conditions necessary for a GE-filter to be a voluntary GE-filter are<br />considered. The GE-filter generated by a given subset is established, and its shape is identifiedhttps://jas.shahroodut.ac.ir/article_2320_d3dbe1e21cedb80b82201fd26488d9bd.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901VALUED-POTENT (GENERAL) MULTIRINGS4968232110.22044/jas.2021.10499.1517ENM.HamidiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.0000-0002-8686-6942A. A.TavakoliDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.R.AmeriSchool of Mathematics, Statistics and Computer Sciences, University of Tehran,
P.O. Box 14155-6455, Tehran, Iran.Journal Article20210124Abstract. This paper extends multirings to a novel concept as general multirings, investigates their properties and presents a special general multirings as notation of (m; n)-potent general multirings. This study analyzes the differences between class of multirings, general multirings and general hyperrings and constructs the class of (in)finite general multirings based on any given non-empty set. In final, we define the concept of hyperideals in general multirings and compare with hyperideals in other<br />similar (hyper)structures.https://jas.shahroodut.ac.ir/article_2321_67c9024c4327e1ad25c24085bc609cb9.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901A NOTE ON RELATIVE GENERALIZED COHEN-MACAULAY MODULES6978232210.22044/jas.2021.10593.1523ENA.Ghanbari DoustFaculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box
1561836314, Tehran, Iran.Journal Article20210224Let a be a proper ideal of a ring R. A finitely generated R-module M is said to be a-relative generalized Cohen-Macaulay if f_a (M)=cd(a ,M). In this note, we introduce a suitable notion of length of a module to characterize the above mentioned modules. Also certain syzygy modules over a relative Cohen-Macaulay ring are studied.https://jas.shahroodut.ac.ir/article_2322_3df4013a02f82f54544c5a30e6f0ace7.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901H-SETS AND APPLICATIONS ON Hv-GROUPS7993232310.22044/jas.2021.10501.1518ENS.Ostadhadi-DehkordiDepartment of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar
Abbas, Iran.T.VougiouklisSchool of Science of Education, Democritus University of Thrace, P.O. Box 68100,
Alexandroupolis, Greece.K.HilaDepartment of Mathematics Engineering, Polytechnic University of Tirana, Tirana,
P.O. Box 1001, Albania.0000-0001-6425-2619Journal Article20210125In this paper, the notion of H-sets on Hv-groups is introduced and some related properties are investigated and some examples are given. In this regards, the concept of regular, strongly regular relations and homomorphism of H-sets are adopted. Also, the classical isomorphism theorems of groups are generalized to H-sets on Hv-groups. Finally, by using these concepts tensor product on Hv-groups is introduced and<br />proved that the tensor product exists and is unique up to isomorphism.https://jas.shahroodut.ac.ir/article_2323_4d3f22f506b926379c168ef5f31fae86.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901GRADED SEMIPRIME SUBMODULES OVER NON-COMMUTATIVE GRADED RINGS95110232410.22044/jas.2021.9102.1442ENP.GhiasvandDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.F.FarzalipourDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.0000-0003-2494-5466Journal Article20191111Let $G$ be a group with identity $e$, $R$ be an associative graded ring and $M$ be a $G$-graded $R$-module. In this article, we intruduce the concept of graded semiprime<br />submodules over non-commutative graded rings. First, we study graded prime $R$-modules<br />over non-commutative graded rings and we get some properties of such graded modules.<br />Second, we study graded semiprime and graded radical submodules of graded $R$-modules.<br />For example, we give some equivalent conditions for a graded module to have zero graded<br />radical submodule.https://jas.shahroodut.ac.ir/article_2324_0c4acb774102cb642394ff5b9a1d337a.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901DIVISOR TOPOLOGIES AND THEIR ENUMERATION111119232510.22044/jas.2021.9712.1473ENF.EsmaeeliDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad, Iran.K.MirzavaziriDepartment of Computer Science, School of Mathematics, Statistics and Computer
Science, University of Tehran, P.O. Box 141556619, Tehran, Iran.M.MirzavaziriDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad, Iran.Journal Article20200527For a positive integer $m$, a subset of divisors of $m$ is called a \textit{divisor topology on $m$} if it contains $1 $ and $m$ and it is closed under taking $\gcd$ and $\rm lcm$. If $m=p_1\dots p_n$ is a square free positive integer, then a divisor topology $m$ corresponds to a topology on the set $[n]=\{1,2,\ldots,n\}$. Giving some facts about divisor topologies, we give a recursive formula for the number of divisor topologies on a positive integer.https://jas.shahroodut.ac.ir/article_2325_51e352c41a02d11fd7a3511d42f35baf.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901NORMAL INJECTIVE RESOLUTION OF GENERAL KRASNER HYPERMODULES121145232610.22044/jas.2021.10188.1505ENM.HamidiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.0000-0002-8686-6942F.FarajiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.R.AmeriSchool of Mathematics, Statistics and Computer Sciences, University of Tehran,
P.O. Box 14155-6455, Tehran, Iran.Kh.Ahmadi-amoliDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.Journal Article20201023In this paper, we construct the concept of general Krasner hyperring based on the ring structures and the left general Krasner hypermodule based on the module structures. This study introduces the trivial left general Krasner hypermodules and proves that the trivial left general Krasner hypermodules are different from left Krasner hypermodules. We show that for any given general Krasner hyperring $R$ and trivial left general Krasner hypermodules $A, B, {\bf_{R}h}$om$(A, B)$ is a left general Krasner hypermodule and ${\bf_{R}h}$om$(-, B)$, $ ({\bf_{R}h}$om$(A, -) )$ is an exact covariant functor (contravariant). Finally, we show that the category ${\bf_{R}GKH}$mod (left trivial general Krasner hypermodules and all (homomorphisms) is an abelian category and trivial left general Krasner hypermodules have a normal injective resolution.https://jas.shahroodut.ac.ir/article_2326_cfdf460f1d5ee4ad171f4f27d432697a.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901SUMS OF UNITS IN SOME CLASSES OF NEAT RINGS147153232710.22044/jas.2021.10905.1536ENN.PouyanDepartment of Mechanical Engineering, University of Shohadaye Hoveizeh Campus
of Technology, Shahid Chamran University of Ahvaz, P.O. Box 64418-78986,
Susangerd, Iran.Journal Article20210616A ring R is said to be clean if every element of R is a sum<br />of an idempotent and a unit. A ring R is a neat ring if every nontrivial<br />homomorphic image is clean. In this paper, first, it is proved that every<br />element of some classes of neat rings is n-tuplet-good if no factor ring<br />of such rings isomorphic to a field of order less than n + 2. Also by considering<br />the structure of FGC rings, it can be proved that some clasess of FGC<br />rings are n-tuplet-good.https://jas.shahroodut.ac.ir/article_2327_f3f2fdb65cf0b4340347c17aaa80279e.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901THE IDENTIFYING CODE NUMBER AND FUNCTIGRAPHS155166232810.22044/jas.2021.9902.1487ENA.ShaminejadDepartment of Mathematics, Imam Khomeini International University, P.O. Box
3414896818, Qazvin, Iran.E.VatandoostDepartment of Mathematics, Imam Khomeini International University, P.O. Box
3414896818, Qazvin, Iran.Journal Article20200714Let G = (V (G); E(G)) be a simple graph. A set D of vertices G is an identifying code of G; if for every two vertices x and y the sets N_G[x] \ D and N_G[y] \ D are non- empty and different. The minimum cardinality of an identifying code in graph G is the identifying code number of G and it is denoted by gamma ID(G): Two vertices x and y are twin, when N_G[x] = N_G[y]: Graphs with at least two twin vertices are not identifiable graphs. In this paper, we deal with identifying code number of functigraph of G: Two upper bounds on identifying code number of functigraph are given. Also, we present some graph G with identifying code number |V (G)| - 2.https://jas.shahroodut.ac.ir/article_2328_b6b4916c4606961fbc5985284ebb2ce2.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901JORDAN HIGHER DERIVATIONS, A NEW APPROACH167177232910.22044/jas.2021.10636.1527ENSayed. Kh.EkramiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.Journal Article20210312Let $ \mathcal{A} $ be a unital algebra over a 2-torsion free commutative ring $ \mathcal{R} $ and $ \mathcal{M} $ be a unital $ \mathcal{A} $-bimodule. We show taht every Jordan higher derivation $ D=\{D_n\}_{n\in \mathbb{N}_0} $ from the trivial extension $ \mathcal{A} \ltimes \mathcal{M} $ into itself is a higher derivation, if $ PD_1(QXP)Q=QD_1(PXQ)P=0 $ for all $ X \in \mathcal{A} \ltimes \mathcal{M} $, in which $ P=(e,0) $ and $ Q=(e^\prime,0) $ for some non-trivial idempotent element $ e \in\mathcal{A} $ and $ e^\prime =1_\mathcal{A}-e $ satisfying the following conditions:<br />$e\mathcal{A}e^\prime\mathcal{A}e=\{0\}$, $e^\prime\mathcal{A}e\mathcal{A}e^\prime=\{0\}$,<br />$e(l.ann_\mathcal{A} \mathcal{M})e=\{0\}$, $e^\prime(r.ann_\mathcal{A} \mathcal{M})e^\prime=\{0\}$<br />and $ eme^\prime=m $ for all $ m \in \mathcal{M} $.https://jas.shahroodut.ac.ir/article_2329_9d17010f447376497c655730b9c58df1.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512810120220901ON THE S_{\lambda}(X) AND {\lambda}-ZERO DIMENSIONAL SPACES179188233010.22044/jas.2021.10906.1535ENS.SoltanpourDepartment of Science, Petroleum University of Technology, P.O. Box 6318714317,
Ahvaz, Iran.0000-0002-1072-9845S.MehranDepartment of Science, Ahvaz Islamic Azad University, P.O. Box 6134937333, Ahvaz,
Iran.Journal Article20210620Let $S_\lambda(X)=\{f\in C(X) : |X\setminus Z(f)|<\lambda\}$, such that $\lambda$ is a regular cardinal<br />number with $\lambda\leq |X|$.<br />It is generalization of $C_F (X)=S_{\aleph_0}(X)$ and<br />$SC_F(X)=S_{\aleph_1}(X)$. Using<br />this concept we extend some of the basic results concerning the socle<br />to $S_\lambda(X)$. It is shown that<br />if $X$ is a $\lambda$-pseudo discrete space, then $C_{K,\lambda}(X)\subseteq S_{\lambda}(X)$.<br />$S_{\lambda}$-completely regular spaces are investigated.<br />Consequently, $X$ is a $S_{\aleph_1}$-completely regular space if and only if $X$ is $\aleph_1$-zero dimensional space.<br />$S_{\lambda}P$-spaces are introduced and studied.https://jas.shahroodut.ac.ir/article_2330_ec85ce47c0b574a150598bd8b7bb24e9.pdf