eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-10-01
3
2
97
107
10.22044/jas.2015.610
610
AMENABILITY OF VECTOR VALUED GROUP ALGEBRAS
Ali Ghaffari
aghaffari@semnan.ac.ir
1
Seyedeh Samaneh Javadi Syahkale
s.javadi62@gmail.com
2
Department of Mathematics, Semnan University, Semnan, Iran
Faculty of Engineering- East Guilan, University of Guilan, Rudsar, Iran
The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).
http://jas.shahroodut.ac.ir/article_610_80140794b33ad022f3303e700e885240.pdf
Amenability
banach algebras
derivation
group algebra
invariant mean
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
109
125
10.22044/jas.2015.611
611
IDEALS IN EL-SEMIHYPERGROUPS ASSOCIATED TO ORDERED SEMIGROUPS
S. H. Ghazavi
s.h.ghazavi@ashrafi.ac.ir
1
S. M. Anvariyeh
anvariyeh@yazd.ac.ir
2
S. Mirvakili
saeed_mirvakili@pnu.ac.ir
3
Department of Mathematics-Yazd University-Yazd-Iran
Department Of Mathematics-Yazd University-Yazd-Iran
Department of Mathematics, Payame Noor University, Tehran, Iran
In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially ordered $Gamma$-semigroup.
http://jas.shahroodut.ac.ir/article_611_edab4a829eab96599e8b252cfea28168.pdf
(m
n)-ideal
interior ideal
Ends lemma
EL-hyperstructures
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
127
131
10.22044/jas.2015.612
612
ON ABSOLUTE CENTRAL AUTOMORPHISMS FIXING THE CENTER ELEMENTWISE
Zahra Kaboutari Farimani
kaboutarizf@gmail.com
1
Mohammad Mehdi Nasrabadi
mnasrabadi@birjand.ac.ir
2
Department of Mathematics, University of Birjand, Birjand, Iran.
Department of Mathematics, University of Birjand, Birjand, Iran.
Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. In this paper we give necessary and sufficient condition on G such that each absolute central automorphism of G fixes the centre element-wise. Also we classify all groups of orders p^3 and p^4 whose absolute central automorphisms fix the centre element-wise.
http://jas.shahroodut.ac.ir/article_612_1811e3d5e5fb09d4b5f4e6ce4fb36612.pdf
absolute centre
absolute central automorphisms
finite p-groups
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
133
146
10.22044/jas.2015.613
613
ON GRADED LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS
Maryam Jahangiri
jahangiri@khu.ac.ir
1
Zohreh Habibbi
z_habibi@pnu.ac.ir
2
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran AND Institute for Research in Fundamental Sciences (IPM) P.O.Box: 19395- 5746, Tehran, Iran.
Department of Mathematics, University of Payame Noor, P.O.Box 19395-3697, Tehran, Iran.
Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^{i}_{R_{+},J}(M)_{n}$.Also, we study the Artinian property and tameness of certainsubmodules and quotient modules of $H^{i}_{R_{+},J}(M)$.
http://jas.shahroodut.ac.ir/article_613_c40acc726617eb0a6a9ca9a12b7a2e55.pdf
graded modules
local cohomology module with respect to a
pair of ideals
Artinian modules
tameness
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
147
150
10.22044/jas.2015.614
614
RESULTS ON ALMOST COHEN-MACAULAY MODULES
A. Mafi
a_mafi@ipm.ir
1
S. Tabejamaat
samanetabejamaat_golestan@yahoo.com
2
Department of Mathematics, University of Kurdistan, P.O.Box 416, Sanandaj, Iran.
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.
http://jas.shahroodut.ac.ir/article_614_d7afaf2c070483f534a968021ba416ea.pdf
Almost Cohen-Macaulay modules
Cohen-Macaulay modules
Ext functors
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
151
169
10.22044/jas.2015.615
615
RATIONAL CHARACTER TABLE OF SOME FINITE GROUPS
H. Shabani
ghorbani30@gmail.com
1
A. R. Ashrafi
ashrafi@kashanu.ac.ir
2
M. Ghorbani
mghorbani@sru.ac.ir
3
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317−51167, I. R. Iran.
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317−51167, I. R. Iran.
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 - 136, I. R. Iran.
The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.
http://jas.shahroodut.ac.ir/article_615_def3b04d2ccfdc9937fb673747390703.pdf
Rational character table
character table
Galois group
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
171
199
10.22044/jas.2015.616
616
MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES
M. H. Hooshmand
hadi.hooshmand@gmail.com
1
Young Researchers and Elite Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are defined in an analogous way.Also, $X$ is magma-joined-magma if it is magma-$x$-magma, for all $xin X$. Therefore, we introduce a big class of basicalgebraic structures with two binary operations which some of theirsub-classes are group-$e$-semigroups, loop-$e$-semigroups, semigroup-$e$-quasigroups,etc. A nice infinite [resp. finite] example for them is real group-grouplike $(mathbb{R},+,0,+_1)$ [resp. Klein group-grouplike].In this paper, I introduce and study the topic, construct several big classes of such algebraic structures and characterizeall identical magma-$e$-magma in several ways. The motivation of this study lies in some interesting connections to $f$-Multiplications, some basic functional equations on algebraic structures and Grouplikes (recently been introduced by the author). At last, we show some of future directionsfor the researches.
http://jas.shahroodut.ac.ir/article_616_129e9f74cb580b363d2f9eb90a41a37f.pdf
08A99
20N02
20M99
20N05
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
201
210
10.22044/jas.2015.618
618
NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS
A. Yousefian Darani
youseffian@gmail.com
1
Department of Mathematics and Applications, University of Mohaghegh Ardabili, P.O.Box 5619911367, Ardabil, Iran.
In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modules are also true for Nonnil-Noetherian modules.
http://jas.shahroodut.ac.ir/article_618_ab7aebe1bfa094cd9b11cca2200588f0.pdf
Noetherian rings
Noetherian modules, Finitely generated submodules, Divided submodules, Phi-modules
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
211
215
10.22044/jas.2015.619
619
A SHORT PROOF OF A RESULT OF NAGEL
N. Shirmohammadi
shirmohammadi@tabrizu.ac.ir
1
Department of Mathematics, University of Tabriz, P.O.Box 51666-16471, Tabriz, Iran.
Let $(R,fm)$ be a Gorenstein local ring and$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are inthe same even liaison class, thenone has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.
http://jas.shahroodut.ac.ir/article_619_3984f444570261f2e3b6227586b24b67.pdf
Linkage
Local cohomology
quasi-Gorenstein module
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-01-01
3
2
217
225
10.22044/jas.2015.620
620
ON THE VANISHING OF DERIVED LOCAL HOMOLOGY MODULES
M. Hatamkhani
m-hatamkhani@araku.ac.ir
1
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran.
Let $R$ be a commutative Noetherian ring, $fa$ anideal of $R$ and $mathcal{D}(R)$ denote the derived category of$R$-modules. For any homologically bounded complex $X$, we conjecture that$sup {bf L}Lambda^{fa}(X)leq$ mag$_RX$. We prove thisin several cases. This generalize the main result of Hatamkhani and Divaani-Aazar cite{HD} for complexes.
http://jas.shahroodut.ac.ir/article_620_374b709d91ba6ee24f3f79fde8febcf8.pdf
Local cohomology modules
local homology modules
magnitude
Noetherian dimension