Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS124143610.22044/jas.2018.6762.1333ENE.HashemiFaculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box
316-3619995161, Shahrood, Iran.Kh.KhalilnezhadDepartment of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran.M.GhadiriDepartment of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran.Journal Article20180207A 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901COTORSION DIMENSIONS OVER GROUP RINGS2532143710.22044/jas.2018.7166.1350ENA.HajizamaniDepartment of Mathematics, University of Hormozgan, P.O. Box 3995, Bandarabbas,
Iran.Journal Article20180617Let $Gamma$ 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901HYPERIDEALS IN M-POLYSYMMETRICAL HYPERRINGS3350143810.22044/jas.2018.6969.1342ENM. A.MadaniDepartment of Mathematics, Payame Noor University, Tehran, Iran.S.MirvakiliDepartment of Mathematics, Payame Noor University, Tehran, Iran.B.DavvazDepartment of Mathematics, Yazd University, Yazd, Iran.Journal Article20180423An 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS5168143910.22044/jas.2018.6939.1340ENM.RezagholibeigiDepartment of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord,
Iran.A. R.NaghipourDepartment of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord,
Iran.0000-0002-7178-6173Journal Article20180406Let $R$ 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901GENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS6982144010.22044/jas.2018.6240.1310ENR.KhanDepartment of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.A.KhanDepartment of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.B.AhmadDepartment of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.R.GulDepartment of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.Journal Article20170921For 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901NEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES8394144110.22044/jas.2018.7007.1345ENZ.NazariDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7713936417,
Rafsanjan, Iran.A.DelbaznasabDepartment of Mathematics, Farhangian University, Yasoj, Iran.M.KamandarDepartment of Mathematics, Shahed University, Tehran, Iran.Journal Article20180506The 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901ON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS95103144210.22044/jas.2018.6789.1334ENR.BayatDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.M.AlaeiyanDepartment of Mathematics, Iran University of Science and Technology, Narmak,
Tehran, Iran.S.FirouzianDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.Journal Article20180213A 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.