Fully primary modules and some variations
A.
Nikseresht
Shiraz University
author
H.
Sharif
Shiraz University
author
text
article
2013
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
1
v.
1
no.
2013
1
17
https://jart.guilan.ac.ir/article_41_49c9e313db9630f99a7306e0d2da6767.pdf
Modules with Noetherian second spectrum
F.
Farshadifar
University of Farhangian
author
text
article
2013
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
1
v.
1
no.
2013
19
30
https://jart.guilan.ac.ir/article_42_2652726182ded6a226c51c0f5cdb9707.pdf
Arens regularity and derivations of Hilbert modules with the certain product
A.
Sahleh
University of Guilan
author
L.
Najarpisheh
University of Guilan
author
text
article
2013
eng
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 $E$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
1
v.
1
no.
2013
31
39
https://jart.guilan.ac.ir/article_43_c935ff4a35e1d9bcd1ab677e11c33519.pdf
On graded almost semiprime submodules
F.
Farzalipour
University of Payame Noor
author
text
article
2013
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
1
v.
1
no.
2013
41
55
https://jart.guilan.ac.ir/article_44_2544963d93ca99d247a7a86068e5e0fa.pdf
On Max-injective modules
R.
Ovlyaee
Kadous Institute of Higher Educations
author
S.
Maleki-Roudposhti
Kadous Institute of Higher Educations
author
text
article
2013
eng
$R$-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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
1
v.
1
no.
2013
57
66
https://jart.guilan.ac.ir/article_45_32d5151408e19b96641d058716a938a1.pdf
On continuous cohomology of locally compact Abelian groups and bilinear maps
H.
Sahleh
University of Guilan
author
text
article
2013
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
1
v.
1
no.
2013
67
77
https://jart.guilan.ac.ir/article_46_2de2cc9120ea26c74a54f5b4acc2febf.pdf