In this paper we investigated some new properties of π-Armendariz rings and studied the relationships between π-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, α-compatible rings and others. We proved that if R is a central Armendariz, then R is π-Armendariz ring. Also we explained how skew Armendariz rings can be ?-Armendariz, for that we proved that if R is a skew Armendariz π-compatible ring, then R is π-Armendariz. Examples are given to illustrate the relations between concepts.

Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

The main objective of this research is to find the coefficient of permeability (k) of the soil and especially clayey soil by finding the degree of consolidation (rate of consolidation). New modify procedure is proposed by using the odometer (consolidation) device. The ordinary conventional permeability test usually takes a long time by preparing and by testing and this could cause some problems especially if there is a need to do a large number of this test and there were a limited number of technicians and/or apparatus. From this point of view the importance of this research is clear, since the modified procedure will require a time of 25 minute only. Derivation made to produce an equation which could be used to fined the permeabi

The work includes synthesis and characterization of some new heterocyclic compounds, as flow: The compound (3) (5-(4-chlorophenyl) -2-hydrazinyl-1,3,4-oxadiazole was synthesized by using two methods; the first method includes the direct reaction between hydrazine hydrate 80% and 5-(4-chlorophenyl)-2- (ethylthio) 1,3,4-oxadiazole (1), the second method involves converting 5-(4-chlorophenyl)-1,3,4-oxadiazol-2-amine (2) to diazonium salt then reducing this salt to compound (3) by stannous chloride. Compound (3) was used as starting material for synthesizing several fused heterocyclic compounds. The compound 6-(4- chlorophenyl)[1,2.4] triazolo [3,4,b][1,3,4] oxadiazole-3-(2H) thione (compound 4) was synthesized from the reaction of compo

Twelve compounds containing a sulphur- or oxygen-based heterocyclic core, 1,3- oxazole or 1,3-thiazole ring with hydroxy, methoxy and methyl terminal substituent, were synthesized and characterized. The molecular structures of these compounds were performed by elemental analysis and different spectroscopic tequniques. The liquid crystalline behaviors were studied by using hot-stage optical polarizing microscopy and differential scanning calorimetry. All compounds of 1,4- disubstituted benzene core with oxazole ring display liquid crystalline smectic A (SmA) mesophase. The compounds of 1,3- and 1,4-disubstituted benzene core with thiazole ring exhibit exclusively enantiotropic nematic liquid crystal phases.

The work includes synthesis and characterization of some new heterocyclic compounds, as flow: The compound (3) (5-(4-chlorophenyl) -2-hydrazinyl-1,3,4-oxadiazole was synthesized by using two methods; the first method includes the direct reaction between hydrazine hydrate 80% and 5-(4-chlorophenyl)-2- (ethylthio) 1,3,4-oxadiazole (1), the second method involves converting 5-(4-chlorophenyl)-1,3,4-oxadiazol-2-amine (2) to diazonium salt then reducing this salt to compound (3) by stannous chloride. Compound (3) was used as starting material for synthesizing several fused heterocyclic compounds. The compound 6-(4-chlorophenyl)[1,2.4] triazolo [3,4,b][1,3,4] oxadiazole-3-(2H) thione (compound 4) was synthesized from the reaction of compound (3)

     This paper develops the work of Mary Florence et.al. on centralizer of semiprime semirings and presents reverse centralizer of semirings with several propositions and lemmas. Also introduces the notion of dependent element and free actions on semirings with some results of free action of centralizer and reverse centralizer on semiprime semirings and some another mappings.

nouns , because deriving these names will lead to eternity which is impossible, and restrict the derivation only in agent nouns from their verbs, and the adjective names from their adjectives with the condition of truth in derivation.
The derivation of “Allah” names was denied due to a creed thoughts, because saying that “Allah” names is derived will not describe the eternal essence of “Allah”, and if it were derived this will make “Allah” is a Compound from his essence and Attributes.
The Al-Zaher people had recant the derivation of the agent nouns by preventing the derivation of “Allah” names because it will make “Allah” is a Compound from his essence and Attributes.
The Al-Zaher people had recant from

Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.