Shahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES141154194210.22044/jas.2019.8245.1402ENM.RahmatiniaDepartment of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179,
Ardabil, Iran.A.Yousefian DaraniDepartment of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179,
Ardabil, Iran.Journal Article20190331The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and obtain the relationship between $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules.https://jas.shahroodut.ac.ir/article_1942_b410589f562e99ad20f1a4a2010554ce.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES155164194310.22044/jas.2020.8830.1428ENA. R.NazariDepartment of Mathematics, Lorestan University, P.O. Box 68151-44316, Khorram
Abad, Iran.F.RastgooDepartment of Mathematics, Lorestan University, P.O. Box 68151-44316, Khorram
Abad, Iran.Journal Article20190818Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of Assh<sub>R</sub> M, then there exists an ideal a of R such that Att<sub>R </sub>H<sup>n</sup>a<sup> </sup>(M)=T. As an application, we give some relationships between top local cohomology modules and top formal local cohomology modules.https://jas.shahroodut.ac.ir/article_1943_da72761077b57d04a475692cca69518c.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101SOME CLASSIFICATIONS OF MONOIDS BY VARIOUS NOTIONS OF INJECTIVITY OF ACTS165180194510.22044/jas.2020.8626.1417ENM.RoueentanLamerd Higher Education Center, Lamerd, Iran.M.ErshadDepartment of Mathematics, College of Sciences, Shiraz University, P.O. Box
71454, Shiraz, Iran.M. A.NaghipoorDepartment of Mathematics, Jahrom University, P.O. Box 74135-11, Jahrom, Iran.Journal Article20190628This paper is a continuation of recent researches concerning generalization of<br /> injectivity of acts over moniods, namely, C-injectivity and InD-injectivity. We introduce new<br /> kinds of injectivity, such as, LC-injectivity and CQ-injectivity. Classications of monoids<br /> by properties of these kinds of injective acts are presented. It is proved that a monoid S<br /> is completely (cyclic) injective if and only if it is completely quasi (CQ-) injective. Some<br /> results on quasi-injective acts are proved. Also new characterizations for right hereditary<br /> monoids and right PP-monoids are given.https://jas.shahroodut.ac.ir/article_1945_b1855eba786ac9866d194c4f31fa871a.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101CONTINUOUS FUNCTIONS ON LG-SPACES181200194610.22044/jas.2020.9599.1471ENA.Rezai AliabadDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.0000-0003-1293-3652H.ZarepourDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20200423By an $l$-generalized topological space, briefly an $LG$-space, we mean the ordered pair $(F,\tau)$ in which $F$ is a frame and $\tau$ is a subframe of $F$. This notion has been first introduced by A.R. Aliabad and A. Sheykhmiri in [$LG$-topology, { <em>Bull</em>. Iran. Math. Soc}., <strong>41</strong> (1), (2015), 239-258]. In this article, we define continuous functions on $LG$-spaces and determine conditions under which the continuous image of a compact element of an $LG$-space is compact. Moreover, we introduce the concept of connectedness for $LG$-spaces and determine conditions under which the continuous image of a connected element of an $LG$-space is connected. In fact, we show that $LG$-spaces are models for topological spaces as well as frames are models for topologies.https://jas.shahroodut.ac.ir/article_1946_7d3a53aeb6d47e5f5a2125390f974935.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101A NOTE ON BALANCED BIG COHEN–MACAULAY MODULES201207194710.22044/jas.2020.9007.1438ENAbdol N.BahlekehDepartment of Mathematics, Gonbad Kavous University, P.O. Box 4971799151,
Gonbad Kavous, Iran.Journal Article20191008Let $(R, m, k)$ be a Cohen-Macaulay complete local ring with the canonical module $\omega$. The aim of this note, is to show that, under mild assumptions, the class of balanced big Cohen--Macaulay modules coincides with the one consisting of those modules admitting a right resolution by modules in $ Add\omega$. This generalizes the well-known result for the class of maximal Cohen--Macaulay modules.https://jas.shahroodut.ac.ir/article_1947_e3aec16656301bf5535c8b9412238431.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH209217194810.22044/jas.2020.8343.1408ENS.AlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran.S.SoltaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, IranJournal Article20190424The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The minimum size of a label class in such a labeling of $G$ with $D(G) = d$ is called the cost of $d$-distinguishing $G$ and is denoted by $\rho_d(G)$. A set of vertices $S\subseteq V(G)$ is a determining set for $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The determining number of $G$, ${\rm Det}(G)$, is the minimum cardinality of determining sets of $G$. In this paper we compute the cost and the determining number for the friendship graphs and corona product of two graphs.https://jas.shahroodut.ac.ir/article_1948_8ed554351047fe89af7fd04bb8a07ed1.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101ON REGULAR PRIME INJECTIVITY OF S-POSETS219230194910.22044/jas.2020.8317.1406ENH.RasouliDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranGh. R.MoghaddasiDepartment of Mathematics, Science and Research Branch, Islamic Azad University,
Tehran, Iran.N.SarvghadDepartment of Mathematics, Hakim Sabzevary University, Sabzevar, Iran.Journal Article20190419In this paper, we define the notion of regular prime monomorphism for $S$-posets over a pomonoid $S$ and investigate some categorical properties including products, coproducts and pullbacks. We study $\mathcal{M}$-injectivity in the category of $S$-posets where $\mathcal{M}$ is the class of regular prime monomorphisms and show that the Skornjakov criterion fails for the regular prime injectivity. Considering a weaker form of such kind of injectivity, we obtain some classifications for pomonoids.https://jas.shahroodut.ac.ir/article_1949_aad563a0d2447906c778a74bfd257d37.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS231250195410.22044/jas.2020.9540.1469ENA.AlhevazFaculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box:
316-3619995161, Shahrood, Iran.0000-0001-6167-607XM.BaghipurDepartment of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar
Abbas, Iran.0000-0002-9069-9243S.PaulDepartment of Applied Sciences, Tezpur University, Tezpur-784028, India.Journal Article20200407The distance signless Laplacian spectral radius of a connected graph $G$ is the largest eigenvalue of the distance signless Laplacian matrix of $G$, defined as $D^{Q}(G)=Tr(G)+D(G)$, where $D(G)$ is the distance matrix of $G$ and $Tr(G)$ is the diagonal matrix of vertex transmissions of $G$. In this paper, we determine some new upper and lower bounds on the distance signless Laplacian spectral radius of $G$ and characterize the extremal graphs attaining these bounds.https://jas.shahroodut.ac.ir/article_1954_3d76b11a1deafa958368655d5c44160b.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101HOOPS WITH QUASI-VALUATION MAPS251268195510.22044/jas.2020.8499.1413ENM.Aaly KologaniHatef Higher Education Institute, P.O. Box 9816848165, Zahedan, Iran.G. R.RezaeiDepartment of Mathematics, University of Sistan and Baluchestan, P.O. Box 98167-
45845, Zahedan, Iran.R. A.BorzooeiDepartment of Mathematics, Shahid Beheshti University, P.O. Box 1983969411,
Tehran, Iran.0000-0001-7538-7885Y. B.JunDepartment of Mathematics, Education, Gyeongsang National University, P.O.
Box 52828, Jinju, Korea.0000-0002-0181-8969Journal Article20190527Based on subalgebras and filters in hoops, the notions of S-quasi-valuation maps and F-quasi-valuation maps are introduced, and related properties are investigated. Relations between S-quasi-valuation maps and F-quasi-valuation maps are introduced. Using F-quasi-valuation map, a (pseudo) metric space is indued, and we show that the operations “⊙”, “→” and “∧” in a hoop are uniformly continuous.https://jas.shahroodut.ac.ir/article_1955_ce7dc383760b98c224e268740b53e849.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101LINKAGE OF IDEALS OVER A MODULE269281195610.22044/jas.2020.9180.1447ENM.JahangiriFaculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box
1561836314, Tehran, Iran.Kh.SayyariFaculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box
1561836314, Tehran, Iran.
Email: sayyarikh@gmail.Journal Article20191211Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered. Specially, we make some extensions and generalizations of a basic result of Peskine and Szpiro \cite[Proposition 1.3]{PS}, namely if $R$ is a Gorenstein local ring, $ a \neq 0$ (an ideal of $R$) and $ b := 0:_R a$ then $\frac{R}{a}$ is Cohen-Macaulay if and only if $\frac{R}{a}$ is unmixed and $\frac{R}{ b}$ is Cohen-Macaulay.https://jas.shahroodut.ac.ir/article_1956_05388a6d1c144832a0ff693aef3886a5.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-512882202101014-CYCLE FREE APM LDPC CODES WITH AN EXPLICIT CONSTRUCTION283289195710.22044/jas.2020.9086.1441ENZ.GholamiDepartment of Mathematics, University of Shahrekord, P.O. Box 8818634141, Shahrekord,
Iran.M.GholamiDepartment of Mathematics, University of Shahrekord, P.O. Box 8818634141, Shahrekord,
Iran.0000-0002-3174-0138Journal Article20191101Recently, a class of low-density parity-check codes<br /> based on affine permutation matrices, called APM-LDPC codes,<br /> have been considered which have some advantages than quasi-cyclic (QC) LDPC codes in terms of minimum-distance, cycle distribution, and error-rate performance. Moreover, some explicit constructions for exponent matrices of conventional APM-LDPC codes<br /> with girth at least 6 have been investigated. In this paper, a class<br /> of 4-cycle free APM-LDPC codes is constructed by a new explicit<br /> method such that the constructed codes have better cycle distributions rather than the recently proposed APM codes with girth 6.<br /> As simulation results show, the constructed codes outperform PEG<br /> and random-like LDPC codes with the same rates and lengths.https://jas.shahroodut.ac.ir/article_1957_2e7bbb3d01640a654c06d6c41e61cedd.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101ON THE CLASS OF ARRAY-BASED APM-LDPC CODES291301195810.22044/jas.2020.8875.1431ENA.NassajMathematics, Sharekord University, Sharekord, IranA. R.NaghipourFaculty of Methematical Sciences
Shahrekord University,
Shahrekord, IranJournal Article20190901We construct an explicit class of affine permutation<br /> matrix low-density parity-check (APM-LDPC) codes based on the<br /> array parity-check matrix by using two affine maps f (x) = x-1 and<br /> g(x) = 2x-1 on Z_m, where m is an odd prime number, with girth 6<br /> and flexible row (column)-weights. Simulation results justify well<br /> performance, minimum-distances and cycle distribution of these<br /> codes in comparison the array-LDPC , structured QC-LDPC and<br /> APM-LDPC.https://jas.shahroodut.ac.ir/article_1958_38d83141b35b9fcbbb6bfd5837381e38.pdf