Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .

    In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of

     In this paper, we study some cases of a common fixed point theorem for classes of firmly nonexpansive and generalized nonexpansive maps. In addition, we establish that the Picard-Mann iteration is faster than Noor iteration and we used Noor iteration to find the solution of delay differential equation.

        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.

This research includes a study of Methylenetetrahydrofolate reductase gene’s allele 677C?T and its correlation with oxidative stress and their impact on female infertility. Fifty infertile women with the range age (23-42) years and twenty five fertile women with the range age (22-39) years as control group living in Erbil city were selected. The serum level of Malondialdehyde (MDA), superoxide dismutase (SOD), prolactin hormone (PRL), Luteinizing hormone (LH), Thyroid stimulating hormone (TSH), Triiodothyronine hormone (T3), and Thyroxine hormone (T4) were measured, also a body mass index (BMI) was calculated. A restriction enzyme (Hinf1) was used to improve the mutation in DNA bands of infertile women. The results showed significant inc

The current study introduces a novel method for calculating the stability time by a new approach based on the conversion of degradation from the conductivity curve results obtained by the conventional method. The stability time calculated by the novel method is shorter than the time measured by the conventional method. The stability time in the novel method can be calculated by the endpoint of the tangency of the conversion curve with the tangent line. This point of tangency represents the stability time, as will be explained in detail. Still, it gives a clear and accurate envisage of the dehydrochlorination behavior and can be generalized to all types of polyvinyl chloride compared to the stability time measured by conventional ones based

Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

The research talks about the concept of investment allocations, showing its linguistic and  idiomatic meaning, as well as the objectives for which the investment allocations are based, as well as the benefits of these allocations since it shows types of investment contracts, including: current and fixed assets and commitment allocations.

 The research has been concluded with several results, including the protection of the banks and the investor. The contracting parties focus on specific dates that both parties are obliged to abide by,  the research also shows the jurisprudence provisions for investment allocations, each ruling according to the specific branch.

Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.

    Let R be a commutative ring with unity and M be a non zero unitary left R-module. M is called a hollow module if every proper submodule N of M is small (N ≪ M), i.e. N + W ≠ M for every proper submodule W in M. A δ-hollow module is a generalization of hollow module, where an R-module M is called δ-hollow module if every proper submodule N of M is δ-small (N δ  M), i.e. N + W ≠ M for every proper submodule W in M with M W is singular. In this work we study this class of modules and give several fundamental properties related with this concept

  In this paper we introduce the notion of semiprime fuzzy module as a generalization of semiprime module. We investigate several characterizations and properties of this concept.