Let R be an individual left R-module of the same type as W, with W being a ring containing one. W’s submodules N and K should be referred to as N and K, respectively that K ⊆ N ⊆ W if N/K <<_J (D_j (W)+K)/K, Then K is known as the D J-coessential submodule of Nin W as K⊆_ (Rce) N. Coessential submodule is a generalization of this idea. These submodules have certain interesting qualities, such that if a certain condition is met, the homomorphic image of D J- N has a coessential submodule called D J-coessential submodule.

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of ri

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings

The title compound, [Ru(C12H7Br2N2)2(CO)2], possesses a distorted octahedral environment about the Ru atom, with two cyclometallated 4,40-dibromoazobenzene ligands and two mutually cis carbonyl ligands. The donor atoms are arranged such that the N atoms are respectively trans to a carbonyl ligand and an aryl C atom. Comment The title compound, (I), has been prepared as a minor product of the reaction of Ru3(CO)12 and 4,40-dibromoazobenzene in refluxing n-octane; the major product is the cluster complex Ru3(3-NC6H4Br)2(CO)9 (Willis et al., 2005). Two strong (CO) absorptions at 2039 and 1991 cm1 in the IR spectrum of (I) are consistent with the presence of two mutually cis carbonyl groups. The crystal structure was investigated to ascertai

        Let R be an associative ring. In this paper we present the definition of (s,t)- Strongly derivation pair and Jordan (s,t)- strongly derivation pair on a ring R, and study the relation between them. Also, we study prime rings, semiprime rings, and rings that have commutator left nonzero divisior with (s,t)- strongly derivation pair, to obtain a (s,t)- derivation. Where s,t: R®R are two mappings of R.

           Let R be  commutative Ring , and let T be  unitary left .In this paper ,WAPP-quasi prime submodules are introduced as  new generalization of Weakly quasi prime submodules , where  proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR , t ϵT, implies that either  r tϵ C +soc   or  s tϵC +soc  .Many examples of characterizations and basic properties are given . Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are established.

         Let R be a commutative ring , the pseudo – von neuman  regular graph of the ring R is define as a graph whose vertex set consists of all elements of R and any two distinct vertices a and b are adjacent if and only if   , this graph denoted by P-VG(R) ,  in this work we got some new results a bout chromatic number of  P-VG(R).

   In this work, the(m-phenylenediamine) and (2-naphthol) have been used in the synthesis of tetradentate ligand [m-phenylenedi(azo-2-naphthol)][H2L] type (N2O2). The ligand was refluxed in the ethanol with the metal ions [Co(II), Cu(II) and Zn(II)] salts, using triethyleamine as a base in (2:2) molar ratio to give the binuclear  complexes. These complexes were characterised by (A.A), F.T.I.R, (U.V-Vis) spectroscopies, along with conductivity, chloride content and melting point measurement. These studies revealed an octahedral geometries for  Co(II), Cu(II) and Zn(II) complexes with the general structure [M2(L)2(H2O)4]. The ligand and its complexes exhibited biological activity against the Bacillus(G+) strain and the

Coupling reaction of 2-amino benzoic acid with the 8-hydroxy quinoline gave the azo ligand (H2L): 5-(2-benzoic acid azo )-8-hydroxy quinoline.Treatment of this ligand with some metal ions (CoII, NiII and CuII ) in ethanolic medium with a (1:2) (M:L) ratio yielded a series of neutral complexes with general Formula[M(HL)2],where: M=Co(II), Ni(II) and Cu(II), HL=anion azo ligand (-1).The prepared complexes were characterized using flame atomic absorption,FT-IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements.