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.

     Let R1be a commutative2ring with identity and M be a unitary R-module. In this6work we7present almost pure8ideal (submodule) concept as a9generalization of pure10ideal (submodule).  lso, we1generalize some9properties of8almost pure ideal (submodule). The 7study is almost regular6ring (R-module).

In this paper, the concept of Jordan triple higher -homomorphisms on prime

rings is introduced.  A result of Herstein is extended on this concept from the ring  into the prime ring .  We prove that every Jordan triple higher -homomorphism of ring  into prime ring  is either triple higher -homomorphism  or triple higher -anti-homomorphism of  into .

We present the concept of maps Γ- periodi2 on Γ -near-ring S. Our main goal is to research and explore the presence and mapping traits such as h Γ –hom anti-Γ –hom, Γ –α-derivations of Γ -periodi2 on Γ- near-rings.

Let M be a prime Γ-ring satisfying abc  abc for all a,b,cM and
,  with center Z, and U be a Lie (Jordan) ideal. A mapping d :M M
is called Γ- centralizing if u d u Z  [ , ( )] for all uU and  .In this paper
, we studied Lie and Jordan ideal in a prime Γ - ring M together with Γ -
centralizing derivations on U.

She noted most of the results of research conducted on the use of computers and the Internet in the areas of administrative, economic, agricultural and educational to a significant improvement in learning outcomes of these groups in the development of mechanisms of action, has increased rates of computer use and applications in various spheres of life at very fast pace so that the computer and the Internet is a vital part of any activity, whether administrative or research or the media, hence it can be said that the use of computers and the Internet in the management of public relations activities in any organization can accelerate the pace of echo positive goals and purposes of public relations, this study comes to looking at us

The compound 3-[4Ì„-(4Ë­-methoxy benzoyloxy) benzylideneamino]-2-thioxo-imidazolidine-4-one [III] was prepared from the cyclization of thiosemicarbazone [II] with
ethyl α -chloroacetate in the presence of fused sodium acetate. Treatment the later compound
with acetic anhydride yielded the corresponding 1-Acetyl-3-[ 4Ì„- (4Ë­- methoxy benzoyloxy)
benzylideneamino] – 2 – thioxo -imidazolidine-4-one [IV]. 1,3-Oxazepine derivatives [V]a-d
and [VI]a-d are obtained from the reaction of compounds[III] and [IV] with different acid
anhydrides, in dry benzene. The FTIR and
1
HNMR spectroscopy are indicated a good
evidence for the formation of the synthesized compounds. Some of the synthesized

 The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals of near-rings and some related properties. Interesting results have been reached, the most prominent of which are the following: Let M be a 3-prime left near-ring and A_1,A_2,…,A_n are nonzero semigroup ideals of M, if d is a right n-derivation of M satisfies on of the following conditions,
d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u ;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=(u_

A variety of liquid crystals comprising heterocyclics 1,3,4-oxadiazol ring [III], aminooxazol [IV]a, and aminothiazol [IV]b were synthesized through a number of steps, beginning of the reaction of 3, 3'- dimethyl - [1, 1'-biphenyl] -4, 4'- diamin, ethyl monochloroacetate and sodium acetate to synthesize diacetate compound[I]. The diester reacted with hydrazine hydrate(N2H4-H2O) to give dihydrazide compound [II], then reacted with Pyruvic acid and phosphorous oxychloride to produce diketone compound [III]. The last compound was reacted with urea and thiourea to give aminooxazol and aminothiazol respectively. The synthesized compounds actually characterized and determined the structures by melting points, FT-IR and 1H-NMR spectroscopies. By u