Let R be an associative ring with identity. An R-module M is called generalized
amply cofinitely supplemented module if every cofinite submodule of M has an
ample generalized supplement in M. In this paper we proved some new results about
this conc- ept.

A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.

    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

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

     The concept of a small f- subm was presented in a previous study. This work introduced a concept of a hollow f- module, where a module is said to be hollow fuzzy when every subm of it is a small f- subm. Some new types of hollow modules are provided namely, Loc- hollow f- modules as a strength of the hollow module, where every Loc- hollow f- module is a hollow module, but the converse is not true. Many properties and characterizations of these concepts are proved, also the relationship between all these types is researched. Many important results that explain this relationship are demonstrated also several characterizations and properties related to these concepts are given.

          This paper deals with studying the effect of hole inclination angle on computing slip velocity and consequently its effect on lifting capacity. The study concentrates on selected vertical wells in Rumaila field, Southern Iraq. Different methods were used to calculate lifting capacity. Lifting capacity is the most important factor for successful drilling and which reflex on preventing hole problems and reduces drilling costs. Many factors affect computing lifting capacity, so hence the effect of hole inclination angle on lifting capacity will be shown in this study. A statistical approach was used to study the lifting capacity values which deal with the effect of hole

Of the many functions that are performed by the drilling fluid, the most important is to transport cuttings from the bit up the annulus to the surface. Various drilling fluid have been widely used in the oil industry to improve lifting capacity. In this study, three mud type have been used which they are, oil base mud, X-anthan polymer and a mixture of CMC and bentonite ,by using Carrying Capacity Index  calculation (CCI) , the Xanthan  gave good values of CCI than other studied drilling fluid. By using Sifferman chart and field data from well in south of Iraq and API equation to find cutting concentration in the annulus, The results showed that the used of thick mud increase the lifting capacity and decrease volumetric drill c

     Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

A submodule Ϝ of an R-module Ε is called small in Ε if whenever  , for some submodule W of Ε , implies  . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if  , such that  , then  , where  is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .

         The main goal of this paper is to give  a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of  purely hollow modules is considered.