ON THE SPECTRUM OF DERANGEMENT GRAPHS OF ORDER A PRODUCT OF THREE PRIMES Modjtaba Ghorbani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, 16785–136, Tehran, Iran. author Mina Rajabi-Parsa Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, 16785–136, Tehran, Iran. author text article 2019 eng A 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 derangementgraph 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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 6 v. 2 no. 2019 81 89 http://jas.shahroodut.ac.ir/article_1359_9e89cef5779fab48c5efd555244f3eb7.pdf dx.doi.org/10.22044/jas.2018.6636.1328 On $\alpha$-semi-Short Modules Maryam Davoudian Department of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box: 6135713895, Ahvaz, Iran. author text article 2019 eng We 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 $\alpha +1$. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 6 v. 2 no. 2019 91 99 http://jas.shahroodut.ac.ir/article_1360_7f4f6f35eeb2298932fcc91ec18e8d44.pdf dx.doi.org/10.22044/jas.2018.5493.1279 ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS Akbar Paad Department of Mathematics, University of Bojnord, P.O.Box 9453155111, Bojnord, Iran. author R. A. Borzooei Department of Mathematics, Shahid Beheshti University, P.O.Box 1983969411, Tehran, Iran author text article 2019 eng In 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.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 ]. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 6 v. 2 no. 2019 101 116 http://jas.shahroodut.ac.ir/article_1361_c9fe9e81d975c704b5be7559a1e0c091.pdf dx.doi.org/10.22044/jas.2018.6130.1305 ON STRONGLY ASSOCIATIVE HYPERRINGS Fatemeh Arabpur Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. author Morteza Jafarpour Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. author text article 2019 eng This paper generalizes the idea of strongly associative hyperoperation introduced in   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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 6 v. 2 no. 2019 117 130 http://jas.shahroodut.ac.ir/article_1362_b14cfdd7b20dd1bac81140e24c087680.pdf dx.doi.org/10.22044/jas.2018.5951.1298 ON THE CAPACITY OF EILENBERG-MACLANE AND MOORE SPACES Mojtaba Mohareri Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O. Box: 1159-91775, Mashhad, Iran. author Behrooz Mashayekhi Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O. Box: 1159-91775, Mashhad, Iran. author Hanieh Mirebrahimi Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O. Box: 1159-91775, Mashhad, Iran. author text article 2019 eng K. 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 ofcompacta. 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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 6 v. 2 no. 2019 131 146 http://jas.shahroodut.ac.ir/article_1363_3d67b550b07ed03fc140c47289cd076b.pdf dx.doi.org/10.22044/jas.2018.6312.1313 ON EQUALITY OF ABSOLUTE CENTRAL AND CLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS Rasoul Soleimani Department of Mathematics, Payame Noor University (PNU), P.O.Box 19395-3697, Tehran, Iran. author text article 2019 eng Let $G$ 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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 6 v. 2 no. 2019 147 155 http://jas.shahroodut.ac.ir/article_1364_aff3c1c2ba782919ee62a881ce5926c0.pdf dx.doi.org/10.22044/jas.2018.6849.1335 ON GRADED INJECTIVE DIMENSION Akram Mahmoodi Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. author Afsaneh Esmaeelnezhad Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. author text article 2019 eng There 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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 6 v. 2 no. 2019 157 167 http://jas.shahroodut.ac.ir/article_1365_4e087ce69ac02696c5bfd84864faa899.pdf dx.doi.org/10.22044/jas.2018.5984.1299