2013
1
1
1
77
Fully primary modules and some variations
2
2
Let R be a commutative ring and M be an Rmodule. We say that M is fully primary, if every proper submodule of M is primary. In this paper, we state some characterizations of fully primary modules. We also give some characterizations of rings over which every module is fully primary, and of those rings over which there exists a faithful fully primary module. Furthermore, we will introduce some variations of fully primary modules and consider similar questions about them.
1

1
17


A.
Nikseresht
Shiraz University
Shiraz University
Iran
ashkan_nikseresht@yahoo.com


H.
Sharif
Shiraz University
Shiraz University
Iran
sharif@susc.ac.ir
Fully primary module
k
primary submodule
kprimary submodule
Modules with Noetherian second spectrum
2
2
Let $R$ be a commutative ring and let $M$ be an $R$module. In this article, we introduce the concept of the Zariski socles of submodules of $M$ and investigate their properties. Also we study modules with Noetherian second spectrum and obtain some related results.
1

19
30


F.
Farshadifar
University of Farhangian
University of Farhangian
Iran
f.farshadifar@gmail.com
Second submodule
second spectrum
Zariski socle
Noetherian spectrum
Arens regularity and derivations of Hilbert modules with the certain product
2
2
Let $A$ be a $C^*$algebra and $E$ be a left Hilbert $A$module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$ is Arens regular. We also study the relationship between derivations of $A$ and $E$.
1

31
39


A.
Sahleh
University of Guilan
University of Guilan
Iran
sahlehj@guilan.ac.ir


L.
Najarpisheh
University of Guilan
University of Guilan
Iran
najarpisheh@phd.guilan.ac.ir
C^{*}
$C^*$algebra
algebra
Hilbert $C^*$module
Banach algebra
Hilbert C^{*}
Arens regular
module
Derivation
On graded almost semiprime submodules
2
2
Let $G$ be a group with identity $e$. Let $R$ be a $G$graded commutative ring with a nonzero identity and $M$ be a graded $R$module. In this article, we introduce the concept of graded almost semiprime submodules. Also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.
1

41
55


F.
Farzalipour
University of Payame Noor
University of Payame Noor
Iran
f_farzalipour@pnu.ac.ir
Graded almost semiprime
graded multiplication module
graded weakly semiprime
On Maxinjective modules
2
2
$R$module. In this paper, we explore more properties of $Max$injective modules and we study some conditions under which the maximal spectrum of $M$ is a $Max$spectral space for its Zariski topology.
1

57
66


R.
Ovlyaee
Kadous Institute of Higher Educations
Kadous Institute of Higher Educations
Iran
ovlyaee@yahoo.ca


S.
MalekiRoudposhti
Kadous Institute of Higher Educations
Kadous Institute of Higher Educations
Iran
sepidehmaleki.r@gmail.com
Max
prime submodule
injective module
$Max$injective module
$Max$weak multiplication module
weak multiplication module
$Max$spectral space
spectral space
On continuous cohomology of locally compact Abelian groups and bilinear maps
2
2
Let $A$ be an abelian topological group and $B$ a trivial topological $A$module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can be embedded in the second bilinear cohomology.
1

67
77


H.
Sahleh
University of Guilan
University of Guilan
Iran
sahleh@guilan.ac.ir
Bilinear cohomology
central extension
nilpotent of class two