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 [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.
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