University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
1
1
2013
11
01
Fully primary modules and some variations
1
17
EN
A.
Nikseresht
Shiraz University
ashkan_nikseresht@yahoo.com
H.
Sharif
Shiraz University
sharif@susc.ac.ir
Let R be a commutative ring and M be an R-module. 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.
Fully primary module,k,primary submodule,k-primary submodule
https://jart.guilan.ac.ir/article_41.html
https://jart.guilan.ac.ir/article_41_49c9e313db9630f99a7306e0d2da6767.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
1
1
2013
11
01
Modules with Noetherian second spectrum
19
30
EN
F.
Farshadifar
University of Farhangian
f.farshadifar@gmail.com
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.
Second submodule,second spectrum,Zariski socle,Noetherian spectrum
https://jart.guilan.ac.ir/article_42.html
https://jart.guilan.ac.ir/article_42_2652726182ded6a226c51c0f5cdb9707.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
1
1
2013
11
01
Arens regularity and derivations of Hilbert modules with the certain product
31
39
EN
A.
Sahleh
University of Guilan
sahlehj@guilan.ac.ir
L.
Najarpisheh
University of Guilan
najarpisheh@phd.guilan.ac.ir
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 $E$.
C^{*},$C^*$-algebra,algebra,Hilbert $C^*$-module,Banach algebra,Hilbert C^{*},Arens regular,module,Derivation
https://jart.guilan.ac.ir/article_43.html
https://jart.guilan.ac.ir/article_43_c935ff4a35e1d9bcd1ab677e11c33519.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
1
1
2013
11
01
On graded almost semiprime submodules
41
55
EN
F.
Farzalipour
University of Payame Noor
f_farzalipour@pnu.ac.ir
Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with a non-zero 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.
Graded almost semiprime,graded multiplication module,graded weakly semiprime
https://jart.guilan.ac.ir/article_44.html
https://jart.guilan.ac.ir/article_44_2544963d93ca99d247a7a86068e5e0fa.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
1
1
2013
11
01
On Max-injective modules
57
66
EN
R.
Ovlyaee
Kadous Institute of Higher Educations
ovlyaee@yahoo.ca
S.
Maleki-Roudposhti
Kadous Institute of Higher Educations
sepidehmaleki.r@gmail.com
$R$-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.
Max,prime submodule,injective module,$Max$-injective module,$Max$-weak multiplication module,weak multiplication module,$Max$-spectral space,spectral space
https://jart.guilan.ac.ir/article_45.html
https://jart.guilan.ac.ir/article_45_32d5151408e19b96641d058716a938a1.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
1
1
2013
11
01
On continuous cohomology of locally compact Abelian groups and bilinear maps
67
77
EN
H.
Sahleh
University of Guilan
sahleh@guilan.ac.ir
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.
Bilinear cohomology,central extension,nilpotent of class two
https://jart.guilan.ac.ir/article_46.html
https://jart.guilan.ac.ir/article_46_2de2cc9120ea26c74a54f5b4acc2febf.pdf