Shahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101ON THE SPECTRUM OF DERANGEMENT GRAPHS OF ORDER A PRODUCT OF THREE PRIMES8189135910.22044/jas.2018.6636.1328ENModjtaba GhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, 16785–136, Tehran, Iran.Mina Rajabi-ParsaDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, 16785–136, Tehran, Iran.Journal Article20180113A permutation with no fixed points is called a derangement. The subset $\mathcal{D}$ of a permutation group is derangement if all elements of $\mathcal{D}$ are derangement. Let $G$ be a permutation group, a derangement<br />graph is one with vertex set $G$ and derangement set $\mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.<br /><br />https://jas.shahroodut.ac.ir/article_1359_9e89cef5779fab48c5efd555244f3eb7.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101On $\alpha $-semi-Short Modules9199136010.22044/jas.2018.5493.1279ENMaryam DavoudianDepartment of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box:
6135713895, Ahvaz, Iran.0000-0003-3433-2444Journal Article20170311We introduce and study the concept of $\alpha $-semi short modules. Using this concept we extend some of the basic results of $\alpha $-short modules to $\alpha $-semi short modules. We observe that if $M$ is an $\alpha $-semi short module then the dual perfect dimension of $M$ is $\alpha $ or $\alpha +1$. %In particular, if a semiprime ring $R$ is $\alpha $-semi short as an $R$-module, then its Noetherian dimension either is $\alpha$ or $\alpha +1$.<br /><br />https://jas.shahroodut.ac.ir/article_1360_7f4f6f35eeb2298932fcc91ec18e8d44.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS101116136110.22044/jas.2018.6130.1305ENAkbar PaadDepartment of Mathematics, University of Bojnord, P.O.Box 9453155111, Bojnord,
Iran.R. A. BorzooeiDepartment of Mathematics, Shahid Beheshti University, P.O.Box 1983969411,
Tehran, Iran0000-0001-7538-7885Journal Article20170816In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G\"{o} del algebra. Specially, we prove that in a G\"{o}del algebra, any fantastic filter is a semi maximal filter and any semi maximal filter is an (n-fold) positive implicative filter. Also, in a $BL$-algebra, any semi maximal and implicative filter is a positive implicative filter.<br />Finally, we give an answer to the open problem in [S. Motamed, L. Torkzadeh, A. Borumand Saeid and N. Mohtashamnia, Radical of filters in BL-algebras, Math. Log. Quart. 57, No. 2, (2011), 166-179 ].https://jas.shahroodut.ac.ir/article_1361_c9fe9e81d975c704b5be7559a1e0c091.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101ON STRONGLY ASSOCIATIVE HYPERRINGS117130136210.22044/jas.2018.5951.1298ENFatemeh ArabpurDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Morteza JafarpourDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20170630This paper generalizes the idea of strongly associative hyperoperation introduced in [7] to the class of hyperrings. We introduce and investigate hyperrings of type 1, type 2 and SDIS. Moreover, we study some examples of these hyperrings and give a new kind of hyperrings called totally hyperrings. Totally hyperrings give us a characterization of Krasner hyperrings. Also, we investigate these strongly hyperoperations in hyperring of series.https://jas.shahroodut.ac.ir/article_1362_b14cfdd7b20dd1bac81140e24c087680.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101ON THE CAPACITY OF EILENBERG-MACLANE AND MOORE SPACES131146136310.22044/jas.2018.6312.1313ENMojtaba MohareriDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic
Structures, Ferdowsi University of Mashhad, P.O. Box: 1159-91775, Mashhad, Iran.Behrooz MashayekhiDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic
Structures, Ferdowsi University of Mashhad, P.O. Box: 1159-91775, Mashhad, Iran.0000-0001-5243-0641Hanieh MirebrahimiDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic
Structures, Ferdowsi University of Mashhad, P.O. Box: 1159-91775, Mashhad, Iran.Journal Article20171014K. Borsuk in 1979, at the Topological Conference in Moscow, introduced concept of the capacity of a compactum and asked some questions concerning properties of the capacity of<br />compacta. In this paper, we give partial positive answers to three of these questions in some cases. In fact, by describing spaces homotopy dominated by Moore and Eilenberg-MacLane spaces, the capacities of a Moore space $M(A,n)$ and an Eilenberg-MacLane space $K(G,n)$ could be obtained. Also, we compute the capacity of wedge sum of finitely many Moore spaces of different degrees and the capacity of product of finitely many Eilenberg-MacLane spaces of different homotopy types. In particular, we compute the capacity of wedge sum of finitely many spheres of the same or different dimensions.<br /><br />https://jas.shahroodut.ac.ir/article_1363_3d67b550b07ed03fc140c47289cd076b.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101ON EQUALITY OF ABSOLUTE CENTRAL AND CLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS147155136410.22044/jas.2018.6849.1335ENRasoul SoleimaniDepartment of Mathematics, Payame Noor University (PNU), P.O.Box 19395-3697,
Tehran, Iran.Journal Article20180311Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $\Aut^{L}(G)$ and $\Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $\Aut_c(G)=\Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^n (n\leq 5)$, for which every absolute central automorphism is class preserving.<br /><br />https://jas.shahroodut.ac.ir/article_1364_aff3c1c2ba782919ee62a881ce5926c0.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101ON GRADED INJECTIVE DIMENSION157167136510.22044/jas.2018.5984.1299ENAkram MahmoodiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.Afsaneh EsmaeelnezhadDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
4697, Tehran, Iran.Journal Article20170710There are remarkable relations between the graded homological dimensions and the ordinary homological dimensions. In this paper, we study the injective dimension of a complex of graded modules and derive its some properties. In particular, we define the $^*$dualizing complex for a graded ring and investigate its consequences.https://jas.shahroodut.ac.ir/article_1365_4e087ce69ac02696c5bfd84864faa899.pdf