Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 7 1 2019 09 01 BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS 1 24 EN E. Hashemi Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-3619995161, Shahrood, Iran. eb_hashemi@yahoo.com Kh. Khalilnezhad Department of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran. kh.khalilnezhad@stu.yazd.ac.ir M. Ghadiri Department of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran. mghadiri@yazd.ac.ir 10.22044/jas.2018.6762.1333 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.<br />(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. <br />(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 http://jas.shahroodut.ac.ir/article_1436.html http://jas.shahroodut.ac.ir/article_1436_dcec6514a4a543ebb30256aaf152b2ad.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 7 1 2019 09 01 COTORSION DIMENSIONS OVER GROUP RINGS 25 32 EN A. Hajizamani Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandarabbas, Iran. hajizamani@hormozgan.ac.ir 10.22044/jas.2018.7166.1350 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 http://jas.shahroodut.ac.ir/article_1437.html http://jas.shahroodut.ac.ir/article_1437_315d3ce1c425b6bc3ed88b4eefa39ca6.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 7 1 2019 09 01 HYPERIDEALS IN M-POLYSYMMETRICAL HYPERRINGS 33 50 EN M. A. Madani Department of Mathematics, Payame Noor University, Tehran, Iran. madani3132003@yahoo.com S. Mirvakili Department of Mathematics, Payame Noor University, Tehran, Iran. saeed_mirvakili@pnu.ac.ir B. Davvaz Department of Mathematics, Yazd University, Yazd, Iran. davvaz@yazd.ac.ir 10.22044/jas.2018.6969.1342 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 http://jas.shahroodut.ac.ir/article_1438.html http://jas.shahroodut.ac.ir/article_1438_b37c329d5e881f5d1d0ab6d53b4ebe5f.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 7 1 2019 09 01 ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS 51 68 EN M. Rezagholibeigi Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran. qolibeigi.meysam@gmail.com A. R. Naghipour 0000-0002-7178-6173 Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran. naghipourar@yahoo.com 10.22044/jas.2018.6939.1340 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 http://jas.shahroodut.ac.ir/article_1439.html http://jas.shahroodut.ac.ir/article_1439_ebb88b5d1aeb02a640e428d56a015c93.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 7 1 2019 09 01 GENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS 69 82 EN R. Khan Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan. raeeskhatim@yahoo.com A. Khan Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan. azhar4set@yahoo.com B. Ahmad Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan. pirbakhtiarbacha@gmail.com R. Gul Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan. roziagul1993@gmail.com 10.22044/jas.2018.6240.1310 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 http://jas.shahroodut.ac.ir/article_1440.html http://jas.shahroodut.ac.ir/article_1440_9fb818b35cb4a812855afbc3bd816fd1.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 7 1 2019 09 01 NEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES 83 94 EN Z. Nazari Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran. znazarirobati@gmail.com A. Delbaznasab Department of Mathematics, Farhangian University, Yasoj, Iran. delbaznasab@gmail.com M. Kamandar Department of Mathematics, Shahed University, Tehran, Iran. kamandar.mahdi@gmail.com 10.22044/jas.2018.7007.1345 ‎‎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 http://jas.shahroodut.ac.ir/article_1441.html http://jas.shahroodut.ac.ir/article_1441_9692022631d2c6707ac622d360bde6c6.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 7 1 2019 09 01 ON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS 95 103 EN R. Bayat Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. r.bayat.tajvar@gmail.com M. Alaeiyan Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran. alaeiyan@iust.ac.ir S. Firouzian Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. siamfirouzian@pnu.ac.ir 10.22044/jas.2018.6789.1334 A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representation<br />R(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 http://jas.shahroodut.ac.ir/article_1442.html http://jas.shahroodut.ac.ir/article_1442_267af50d206373aeaaa0fe17235b3920.pdf