Shahrood University of Technology Journal of Algebraic Systems 2345-5128 6 2 2019 01 01 ON THE SPECTRUM OF DERANGEMENT GRAPHS OF ORDER A PRODUCT OF THREE PRIMES 81 89 1359 10.22044/jas.2018.6636.1328 EN Modjtaba Ghorbani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, 16785–136, Tehran, Iran. Mina Rajabi-Parsa Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, 16785–136, Tehran, Iran. Journal Article 2018 01 13 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 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.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 6 2 2019 01 01 On $\alpha$-semi-Short Modules 91 99 1360 10.22044/jas.2018.5493.1279 EN Maryam Davoudian Department of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box: 6135713895, Ahvaz, Iran. Journal Article 2017 03 11 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 $\alpha +1$.<br /><br /> https://jas.shahroodut.ac.ir/article_1360_7f4f6f35eeb2298932fcc91ec18e8d44.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 6 2 2019 01 01 ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS 101 116 1361 10.22044/jas.2018.6130.1305 EN Akbar Paad Department of Mathematics, University of Bojnord, P.O.Box 9453155111, Bojnord, Iran. R. A. Borzooei Department of Mathematics, Shahid Beheshti University, P.O.Box 1983969411, Tehran, Iran 0000-0001-7538-7885 Journal Article 2017 08 16 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.<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.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 6 2 2019 01 01 ON STRONGLY ASSOCIATIVE HYPERRINGS 117 130 1362 10.22044/jas.2018.5951.1298 EN Fatemeh Arabpur Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. Morteza Jafarpour Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. Journal Article 2017 06 30 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. https://jas.shahroodut.ac.ir/article_1362_b14cfdd7b20dd1bac81140e24c087680.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 6 2 2019 01 01 ON THE CAPACITY OF EILENBERG-MACLANE AND MOORE SPACES 131 146 1363 10.22044/jas.2018.6312.1313 EN 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. 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. 0000-0001-5243-0641 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. Journal Article 2017 10 14 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 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.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 6 2 2019 01 01 ON EQUALITY OF ABSOLUTE CENTRAL AND CLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS 147 155 1364 10.22044/jas.2018.6849.1335 EN Rasoul Soleimani Department of Mathematics, Payame Noor University (PNU), P.O.Box 19395-3697, Tehran, Iran. Journal Article 2018 03 11 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.<br /><br /> https://jas.shahroodut.ac.ir/article_1364_aff3c1c2ba782919ee62a881ce5926c0.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 6 2 2019 01 01 ON GRADED INJECTIVE DIMENSION 157 167 1365 10.22044/jas.2018.5984.1299 EN Akram Mahmoodi Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. Afsaneh Esmaeelnezhad Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. Journal Article 2017 07 10 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. https://jas.shahroodut.ac.ir/article_1365_4e087ce69ac02696c5bfd84864faa899.pdf