@article { author = {Nikseresht, A. and Sharif, H.}, title = {Fully primary modules and some variations}, journal = {Journal of Algebra and Related Topics}, volume = {1}, number = {1}, pages = {1-17}, year = {2013}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, abstract = {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.}, keywords = {Fully primary module,k,primary submodule,k-primary submodule}, url = {https://jart.guilan.ac.ir/article_41.html}, eprint = {https://jart.guilan.ac.ir/article_41_49c9e313db9630f99a7306e0d2da6767.pdf} } @article { author = {Farshadifar, F.}, title = {Modules with Noetherian second spectrum}, journal = {Journal of Algebra and Related Topics}, volume = {1}, number = {1}, pages = {19-30}, year = {2013}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, abstract = {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.}, keywords = {Second submodule,second spectrum,Zariski socle,Noetherian spectrum}, url = {https://jart.guilan.ac.ir/article_42.html}, eprint = {https://jart.guilan.ac.ir/article_42_2652726182ded6a226c51c0f5cdb9707.pdf} } @article { author = {Sahleh, A. and Najarpisheh, L.}, title = {Arens regularity and derivations of Hilbert modules with the certain product}, journal = {Journal of Algebra and Related Topics}, volume = {1}, number = {1}, pages = {31-39}, year = {2013}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, abstract = {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 $E$.}, keywords = {C^{*},$C^*$-algebra,algebra,Hilbert $C^*$-module,Banach algebra,Hilbert C^{*},Arens regular,module,Derivation}, url = {https://jart.guilan.ac.ir/article_43.html}, eprint = {https://jart.guilan.ac.ir/article_43_c935ff4a35e1d9bcd1ab677e11c33519.pdf} } @article { author = {Farzalipour, F.}, title = {On graded almost semiprime submodules}, journal = {Journal of Algebra and Related Topics}, volume = {1}, number = {1}, pages = {41-55}, year = {2013}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, abstract = {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.}, keywords = {Graded almost semiprime,graded multiplication module,graded weakly semiprime}, url = {https://jart.guilan.ac.ir/article_44.html}, eprint = {https://jart.guilan.ac.ir/article_44_2544963d93ca99d247a7a86068e5e0fa.pdf} } @article { author = {Ovlyaee, R. and Maleki-Roudposhti, S.}, title = {On Max-injective modules}, journal = {Journal of Algebra and Related Topics}, volume = {1}, number = {1}, pages = {57-66}, year = {2013}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, abstract = {$R$-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.}, keywords = {Max,prime submodule,injective module,$Max$-injective module,$Max$-weak multiplication module,weak multiplication module,$Max$-spectral space,spectral space}, url = {https://jart.guilan.ac.ir/article_45.html}, eprint = {https://jart.guilan.ac.ir/article_45_32d5151408e19b96641d058716a938a1.pdf} } @article { author = {Sahleh, H.}, title = {On continuous cohomology of locally compact Abelian groups and bilinear maps}, journal = {Journal of Algebra and Related Topics}, volume = {1}, number = {1}, pages = {67-77}, year = {2013}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, abstract = {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.}, keywords = {Bilinear cohomology,central extension,nilpotent of class two}, url = {https://jart.guilan.ac.ir/article_46.html}, eprint = {https://jart.guilan.ac.ir/article_46_2de2cc9120ea26c74a54f5b4acc2febf.pdf} }