Let S be a prime inverse semiring with center Z(S). The aim of this research is to prove some results on the prime inverse semiring with (α, β) – derivation that acts as a homomorphism or as an anti- homomorphism, where α, β are automorphisms on S.

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.

     Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between prime submodules of a given module and the extension of prime submodules. The relations between prime submodules of two given modules and the prime submodules in the direct product of their quotient module are studied and investigated.

In this study, we introduce and study the concepts of generalized ( , )-reverse derivation, Jordan generalized ( , )-reverse derivation, and Jordan generalized triple ( , )-reverse derivation from Γ-semiring S into ΓS-module X.  The most important findings of this paper are as follows:

If S is Γ-semiring and X is ΓS-module, then every Jordan generalized ( , )- reverse derivations from S into X associated with Jordan ( , )-reverse derivation d from S into X is ( , )-reverse derivation from S into X.

     Let  be a commutative  ring with identity , and  be a unitary (left) R-module. A proper submodule  of  is said to be quasi- small prime submodule  , if whenever   with  and , then either or . In this paper ,we give a comprehensive study of quasi- small prime submodules.

      This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.

  In this work we shall introduce the concept of weakly quasi-prime modules and give some properties of this type of modules.

A series of new 1,8-naphthalimides linked to azetidinone, thiazolidinone or tetrazole moieties were synthesized. N-ester-1,8-naphthalimide (1) was obtained by direct imidation of 1,8-naphthalic anhydride with ethylglycinate. Compound (1) was treated with hydrazine hydrate in absolute ethanol to give N-acetohydrazide-1,8-naphthalimide (2). The hydrazine derivative (2) was used to obtain new Schiff bases (3-7). Three routes with different reagents were used for the cyclization of the prepared Schiff bases. Fifteen cyclic Schiff bases (8-22) with four- and five-membered rings were obtained.
The structures of the newly synthesized compounds were identified by their FTIR, 1H-NMR, 13C-NMR spectral data and some physical properties. Furtherm

In this paper, we study the class of prime semimodules and the related concepts, such as the class of  semimodules, the class of Dedekind semidomains, the class of prime semimodules which is invariant subsemimodules of its injective hull, and the compressible semimodules. In order to make the work as complete as possible, we stated, and sometimes proved, some known results related to the above concepts.