let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

Existing researches suggest that the code clone (duplicated code) is one of the factors that degrades the design and the structure of software and lowers the software quality such as readability and changeability. However, the influence of code clones on software quality has not been quantitatively clarified yet. In this paper, we have tried to quantitatively clarify the relation between code c...

Abstract Let $${{\mathcal {S}}}{{\mathcal {S}}}$$ S and {C}}}$$ C be the strictly singular cosingular operators acting between Banach spaces, let $$P\Phi _+$$ P Φ + perturbation classes for upper ...

It is shown that the BRST operator of twisted N = 4 Yang-Mills theory in four dimensions is locally the same as the BRST operator of a fully decomposed non-Abelian gerbe. Using locally defined Yang-Mills theories we describe non-perturbative backgrounds that carry a novel magnetic flux. Given by elements of the crossed module G ⋉ AutG, these nongeometric fluxes can be classified in terms of the...

In this work, performance of hollow fiber membrane photobioreactor (HFMPB) on the growth of Dunaliella Salina (G26) at various aeration rates (0.1 and 0.2 VVm) and medium re-circulation flow rates (500 and 1000 mL/h) were studied. Cultivation was carried out at both batch and semi-continuous modes in HFMPBs containing neat and hydrophilized in-house fabricated poly ethylene (PE) membranes at fi...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

Let C be a non-empty class of modules closed under isomorphic copies. We consider some classes of modules associated to C. Among them, we study two important classes in the theory of natural and conatural classes of modules, namely the class consisting of all modules having no non-zero submodule in C, as well as its dual.