Let  be a commutative ring with an identity and be a unitary -module. We say that a non-zero submodule  of  is  primary if for each with en either or  and an -module  is a small primary if   =  for each proper submodule  small in. We provided and demonstrated some of the characterizations and features of these types of submodules (modules).  

In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

Let R be a 2-torision free prime ring and ?, ?? Aut(R). Furthermore, G: R×R?R is a symmetric generalized (?, ?)-Biderivation associated with a nonzero (?, ?)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

  Let R be an associative ring with identity and M a non – zero unitary R-module.In this paper we introduce the definition of purely co-Hopfian module, where an R-module M is said to be purely co-Hopfian if for any monomorphism f Ë› End (M), Imf is pure in M and we give  some properties of this kind of modules.

In the present work the performance of semifluidized bed adsorber was evaluated for removal of phenolic compound from wastewater using commercial activated carbon as adsorbent. P-chlorophenol (4-Chlorophenol) and o-cresol (2-methylphenol) was selected as a phenolic compound for that purpose. The phenols percent removal, in term of breakthrough curves were studied as affected by hydrodynamics limitations which include minimum and maximum semifluidization velocities and packed bed formation in the column by varying various parameters such as inlet liquid superficial velocity (from U_minsf to 8U_minsf m/s), and retaining grid (sometimes referred to as adsorbent loading) to initial static bed height ratio (from 3-4.5). In

The aim of this paper is to introduce and study the concept of SN-spaces via the notation of simply-open sets as well as to investigate their relationship to other topological spaces and give some of its properties.

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.