eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2019-09-01
7
1
1
24
10.22044/jas.2018.6762.1333
1436
BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS
E. Hashemi
eb_hashemi@yahoo.com
1
Kh. Khalilnezhad
kh.khalilnezhad@stu.yazd.ac.ir
2
M. Ghadiri
mghadiri@yazd.ac.ir
3
Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-3619995161, Shahrood, Iran.
Department of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran.
Department of Mathematics, University of Yazd, P.O. Box 89195-741, Yazd, Iran.
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.
http://jas.shahroodut.ac.ir/article_1436_dcec6514a4a543ebb30256aaf152b2ad.pdf
Delta-quasi-Baer rings
Sigma-quasi-Baer rings
Skew PBW extensions
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2019-09-01
7
1
25
32
10.22044/jas.2018.7166.1350
1437
COTORSION DIMENSIONS OVER GROUP RINGS
A. Hajizamani
hajizamani@hormozgan.ac.ir
1
Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandarabbas, Iran.
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.
http://jas.shahroodut.ac.ir/article_1437_315d3ce1c425b6bc3ed88b4eefa39ca6.pdf
cotorsion dimension
global cotorsion dimension
perfect ring
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2019-09-01
7
1
33
50
10.22044/jas.2018.6969.1342
1438
HYPERIDEALS IN M-POLYSYMMETRICAL HYPERRINGS
M. A. Madani
madani3132003@yahoo.com
1
S. Mirvakili
saeed_mirvakili@pnu.ac.ir
2
B. Davvaz
davvaz@yazd.ac.ir
3
Department of Mathematics, Payame Noor University, Tehran, Iran.
Department of Mathematics, Payame Noor University, Tehran, Iran.
Department of Mathematics, Yazd University, Yazd, Iran.
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.
http://jas.shahroodut.ac.ir/article_1438_b37c329d5e881f5d1d0ab6d53b4ebe5f.pdf
M-polysymmetrical hyperring
Hyperideal
Reduced ring
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2019-09-01
7
1
51
68
10.22044/jas.2018.6939.1340
1439
ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS
M. Rezagholibeigi
qolibeigi.meysam@gmail.com
1
A. R. Naghipour
naghipourar@yahoo.com
2
Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran.
Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran.
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.
http://jas.shahroodut.ac.ir/article_1439_ebb88b5d1aeb02a640e428d56a015c93.pdf
Rings
Matrix rings
Jacobson radical
Unit graphs
Unitary Cayley graphs
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2019-09-01
7
1
69
82
10.22044/jas.2018.6240.1310
1440
GENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS
R. Khan
raeeskhatim@yahoo.com
1
A. Khan
azhar4set@yahoo.com
2
B. Ahmad
pirbakhtiarbacha@gmail.com
3
R. Gul
roziagul1993@gmail.com
4
Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.
Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.
Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.
Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.
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.
http://jas.shahroodut.ac.ir/article_1440_9fb818b35cb4a812855afbc3bd816fd1.pdf
Soft sets
N)-uni-soft ideal
(M
N)-uni-soft interior ideals
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2019-09-01
7
1
83
94
10.22044/jas.2018.7007.1345
1441
NEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES
Z. Nazari
znazarirobati@gmail.com
1
A. Delbaznasab
delbaznasab@gmail.com
2
M. Kamandar
kamandar.mahdi@gmail.com
3
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran.
Department of Mathematics, Farhangian University, Yasoj, Iran.
Department of Mathematics, Shahed University, Tehran, Iran.
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.
http://jas.shahroodut.ac.ir/article_1441_9692022631d2c6707ac622d360bde6c6.pdf
Generalized group
Generalized ring
Topological generalized group
Top space
Lie group
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2019-09-01
7
1
95
103
10.22044/jas.2018.6789.1334
1442
ON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS
R. Bayat
r.bayat.tajvar@gmail.com
1
M. Alaeiyan
alaeiyan@iust.ac.ir
2
S. Firouzian
siamfirouzian@pnu.ac.ir
3
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
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.
http://jas.shahroodut.ac.ir/article_1442_267af50d206373aeaaa0fe17235b3920.pdf
hypergraph
t-Cayley hypergraph
normal t-Cayley hypergraph