JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.6762.1333 Original Manuscript BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS Hashemi E. Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-3619995161, Shahrood, Iran. Khalilnezhad Kh. Department of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran. Ghadiri M. Department of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran. 01 09 2019 7 1 1 24 07 02 2018 28 09 2018 Copyright © 2019, Shahrood University of Technology. 2019 http://jas.shahroodut.ac.ir/article_1436.html

A ring \$R\$ with an automorphism \$sigma\$ and a \$sigma\$-derivation \$delta\$ is called \$delta\$-quasi-Baer (resp., \$sigma\$-invariant quasi-Baer) if the right annihilator of every \$delta\$-ideal (resp., \$sigma\$-invariant ideal) of \$R\$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let \$A=sigma(R)leftlangle x_{1},ldots,x_{n}rightrangle \$ be a skew PBW extension of derivation type of a ring \$R\$. (i) It is shown that \$ R\$ is \$Delta\$-quasi-Baer if and only if \$ A\$ is quasi-Baer.(ii) \$ R\$ is \$Delta\$-Baer if and only if \$ A\$ is Baer, when \$R\$ has IFP. Also, let \$A=sigma (R)leftlangle x_1, ldots , x_nrightrangle\$ be a quasi-commutative skew PBW extension of a ring \$R\$. (iii) If \$R\$ is a \$Sigma\$-quasi-Baer ring, then \$A \$ is a quasi-Baer ring. (iv) If \$A \$ is a quasi-Baer ring, then \$R\$ is a \$Sigma\$-invariant quasi-Baer ring. (v) If \$R\$ is a \$Sigma\$-Baer ring, then \$A \$ is a Baer ring, when \$R\$ has IFP. (vi) If \$A \$ is a Baer ring, then \$R\$ is a \$Sigma\$-invariant Baer ring. Finally, we show that if \$A = sigma (R)leftlangle x_1, ldots , x_nrightrangle \$ is a bijective skew PBW extension of a quasi-Baer ring \$R\$, then \$A\$ is a quasi-Baer ring.

Delta-quasi-Baer rings Sigma-quasi-Baer rings Skew PBW extensions
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.7166.1350 Original Manuscript COTORSION DIMENSIONS OVER GROUP RINGS COTORSION DIMENSIONS OVER GROUP RINGS Hajizamani A. Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandarabbas, Iran. 01 09 2019 7 1 25 32 17 06 2018 02 10 2018 Copyright © 2019, Shahrood University of Technology. 2019 http://jas.shahroodut.ac.ir/article_1437.html

Let \$Gamma\$ be a group, \$Gamma'\$ a subgroup of \$Gamma\$ with finite index and \$M\$ be a \$Gamma\$-module. We show that \$M\$ is cotorsion if and only if it is cotorsion as a \$Gamma'\$-module. Using this result, we prove that the global cotorsion dimensions of rings \$ZGamma\$ and \$ZGamma'\$ are equal.

cotorsion dimension global cotorsion dimension perfect ring
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.6969.1342 Original Manuscript HYPERIDEALS IN M-POLYSYMMETRICAL HYPERRINGS Hyperideals in M-polysymmetrical hyperrings Madani M. A. Department of Mathematics, Payame Noor University, Tehran, Iran. Mirvakili S. Department of Mathematics, Payame Noor University, Tehran, Iran. Davvaz B. Department of Mathematics, Yazd University, Yazd, Iran. 01 09 2019 7 1 33 50 23 04 2018 10 10 2018 Copyright © 2019, Shahrood University of Technology. 2019 http://jas.shahroodut.ac.ir/article_1438.html

An M-polysymmetrical hyperring \$(R,+,cdot )\$ is an algebraic system, where \$(R,+)\$ is an M-polysymmetrical hypergroup, \$(R,cdot )\$ is a semigroup and \$cdot\$ is bilaterally distributive over \$+\$. In this paper, we introduce the concept of hyperideals of an M-polysymmetrical hyperring and by using this concept, we construct an ordinary quotient ring. Finally, the fundamental theorem of homomorphism is derived in the context of M-polysymmetrical hyperrings.

M-polysymmetrical hyperring Hyperideal Reduced ring
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.6939.1340 Original Manuscript ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS Rezagholibeigi M. Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran. Naghipour A. R. Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran. 01 09 2019 7 1 51 68 06 04 2018 19 10 2018 Copyright © 2019, Shahrood University of Technology. 2019 http://jas.shahroodut.ac.ir/article_1439.html

Let \$R\$ be a ring (not necessarily commutative) with nonzero identity. We define \$Gamma(R)\$ to be the graph with vertex set \$R\$ in which two distinct vertices \$x\$ and \$y\$ are adjacent if and only if there exist unit elements \$u,v\$ of \$R\$ such that \$x+uyv\$ is a unit of \$R\$. In this paper, basic properties of \$Gamma(R)\$ are studied. We investigate connectivity and the girth of \$Gamma(R)\$, where \$R\$ is a left Artinian ring. We also determine when the graph \$Gamma(R)\$ is a cycle graph. We prove that if \$Gamma(R)congGamma(M_{n}(F))\$ then \$Rcong M_{n}(F)\$, where \$R\$ is a ring and \$F\$ is a finite field. We show that if \$R\$ is a finite commutative semisimple ring and \$S\$ is a commutative ring such that \$Gamma(R)congGamma(S)\$, then \$Rcong S\$. Finally, we obtain the spectrum of \$Gamma(R)\$, where \$R\$ is a finite commutative ring.

Rings Matrix rings Jacobson radical Unit graphs Unitary Cayley graphs
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.6240.1310 Original Manuscript GENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS Generalized uni-soft interior ideals of ordered semigroups Khan R. Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan. Khan A. Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan. Ahmad B. Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan. Gul R. Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan. 01 09 2019 7 1 69 82 21 09 2017 29 10 2018 Copyright © 2019, Shahrood University of Technology. 2019 http://jas.shahroodut.ac.ir/article_1440.html

For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups the concept of (M,N)-uni-soft ideals and the (M,N)-uni-soft interior ideals coincide. Finally, we introduced (M,N)-uni-soft simple ordered semigroup and characterized the simple ordered semigroups in terms of (M,N)-uni-soft interior ideals.

Soft sets N)-uni-soft ideal (M N)-uni-soft interior ideals
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.7007.1345 Original Manuscript NEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES New methods for constructing generalized groups‎, ‎topological‎ ‎generalized groups‎, ‎and Top spaces Nazari Z. Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran. Delbaznasab A. Department of Mathematics, Farhangian University, Yasoj, Iran. Kamandar M. Department of Mathematics, Shahed University, Tehran, Iran. 01 09 2019 7 1 83 94 06 05 2018 29 10 2018 Copyright © 2019, Shahrood University of Technology. 2019 http://jas.shahroodut.ac.ir/article_1441.html

‎‎The purpose of this paper is to introduce new methods for constructing generalized groups, generalized topological groups and top spaces. We study some properties of these structures and present some relative concrete examples. Moreover, we obtain generalized groups by using of Hilbert spaces and tangent spaces of Lie groups, separately.

Generalized group‎ ‎Generalized ring‎ Topological generalized group‎ Top space‎ ‎Lie group
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.6789.1334 Original Manuscript ON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS ON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS Bayat R. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. Alaeiyan M. Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran. Firouzian S. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. 01 09 2019 7 1 95 103 13 02 2018 15 12 2018 Copyright © 2019, Shahrood University of Technology. 2019 http://jas.shahroodut.ac.ir/article_1442.html

A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representationR(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley hypergraphs of abelian groups, where S < 4.

hypergraph t-Cayley hypergraph normal t-Cayley hypergraph