An R-module M is called ET-H-supplemented module if for each submodule X of M, there exists a direct summand D of M, such that T⊆X+K if and only if T⊆D+K, for every essential submodule K of M and T M. Also, let T, X and Y be submodules of a module M , then we say that Y is ET-weak supplemented of X in M if T⊆X+Y and (X⋂Y M. Also, we say that M is ET-weak supplemented module if each submodule of M has an ET-weak supplement in M. We give many characterizations of the ET-H-supplemented module and the ET-weak supplement. Also, we give the relation between the ET-H-supplemented and ET-lifting modules, along with the relationship between the ET weak -supplemented and ET-lifting modules.
Let be a ring with identity and let be a left R-module. If is a proper submodule of and , is called --semi regular element in , If there exists a decoposition such that is projective submodule of and . The aim of this paper is to introduce properties of F-J-semi regular module. In particular, its characterizations are given. Furthermore, we introduce the concepts of Jacobson hollow semi regular module and --semiregular module. Finally, many results of Jacobson hollow semi regular module and --semiregular module are presented.
Let R be a commutative ring with unity .M an R-Module. M is called coprime module (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.
Let
be an
module,
be a fuzzy soft module over
, and
be a fuzzy soft ring over
, then
is called FSFS module if and only if
is an
module. In this paper, we introduce the concept of
Noetherian and
Artinian modules and finally we investigate some basic properties of
Noetherian and
Artinian modules.
Let R be a commutative ring with unity. In this paper we introduce and study the concept of strongly essentially quasi-Dedekind module as a generalization of essentially quasiDedekind module. A unitary R-module M is called a strongly essentially quasi-Dedekind module if ( , ) 0 Hom M N M for all semiessential submodules N of M. Where a submodule N of an R-module M is called semiessential if , 0  pN for all nonzero prime submodules P of M .
The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.
Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXïƒW for all fully invariant R-submodule X of M, implies XïƒW. M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.
The trace elements in the medical herbs play an important role in the treatment of diseases. Well selected herbs samples of Iraqi herbs and collected from local markets. In this study, the concentrations of nine elements Na,K, Zn, Fe ,Co ,Cu ,Ni , Pb and Cd were determined in fourteen kinds herbs common belonging to Matricaria Chamomile Cinnamon,Pimpinella Anisum L., Zea Maize , Anethum Graveolens L., Jeft, Teucrium Polium L., Cagsia Italica,Echium Talicum L.,Ocimum Basilcum L., Galeopsis Sejetum,Nigella Sative L., Cyperus Rotundus L.,Lupinus Jaimehintoniana.The herbs samples were analysed by flameless except Na,K, in flame atomic absorption spectrophotometer in different medical herbs.The results indicated that the Na and K
... Show MoreThe concept of St-Polyform modules, was introduced and studied by Ahmed in [1], where a module M is called St-polyform, if for every submodule N of M and for any homomorphism ð‘“:N M; kerð‘“ is St-closed submodule in N. The novelty of this paper is to dualize this class of modules, the authors call it CSt-polyform modules, and according to this dualizations, some results which appeared in [1] are dualized for example we prove that in the class of hollow modules, every CSt-polyform module is coquasi-Dedekind. In addition, several important properties of CSt-polyform module are established, and other characterization of CSt-polyform is given. Moreover, many relationships of CSt-polyform modules with other related concepts are
... Show MoreThe electrical resistivity method is one of the geophysical methods for detecting weak subsurface zone. The 2D resistivity data were used to compare three electrode configurations, Wenner, Dipole-dipole, and Schlumberger, to detect weak subsurface zones along a profile south of Baghdad near the Bismayah pumping station. The results show many zones of low resistivity that may be weak zones. A dipole-dipole array is a large number of measurements and is more sensitive than others. The Wenner-Schlumberger array has a depth also higher than other arrays. Wenner array has higher signal strength than other arrays. Because it is more sensitive to horizontal and vertical structures, the dipole-dipole array is the optimum for mapping sub
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