In this paper, as generalization of second modules we introduce type of modules namely (essentially second modules). A comprehensive study of this class of modules is given, also many results concerned with this type and other related modules presented.

 In this paper, we give a comprehensive study of min (max)-CS modules such as a closed submodule of min-CS module is min-CS. Amongst other results we show that a direct summand of min (max)-CS module is min (max)-CS module. One of interested theorems in this paper is, if R is a nonsingular ring then R is a max-CS ring if and only if R is a min-CS ring.

In this note we consider a generalization of the notion of a purely extending
modules, defined using y– closed submodules.
We show that a ring R is purely y – extending if and only if every cyclic nonsingular
R – module is flat. In particular every nonsingular purely y extending ring is
principal flat.

An -module  is extending if every submodule of   is essential in a direct summand of . Following Clark, an -module  is purely extending if every submodule of   is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module     is Goldie extending if, for each submodule      of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module  is purely Goldie extending if, for each , there is a pure submodule P of such that  . Many c

  Let R be an associative ring with identity and M a non – zero unitary R-module.In this paper we introduce the definition of purely co-Hopfian module, where an R-module M is said to be purely co-Hopfian if for any monomorphism f Ë› End (M), Imf is pure in M and we give  some properties of this kind of modules.

      The current study involves an experimental investigation of plasma main parameters of a DC discharge with a hollow cathode (HCD) geometry in air using apertures of different diameters from the hollow cathode (1, 1.5, 2, and 2.5 cm). A tiny Langmuir probe is used to investigate the plasma properties. The HCD was operated at constant power of 12.4 W and gas pressures ranging between 0.1 to 0.8 torr. It was observed that the operational conditions strongly affect the electron temperature and density, while the hollow cathode diameter has not much influence. The main important observation was that at relatively high air pressure (>0.4 torr) two electron temperatures were obtained, while at relatively low pressure (<0.4 torr)

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.

PPSU hollow fiber nanofiltration membranes are prepared by applying two concentrations and various extrusion pressures according to the phase inversion method. Cross-sectional area and outer structures were characterized by using scanning electron microscope (SEM) and atomic force microscopy (AFM). In additional to the pore size distribution, either the mean roughness or the mean pore size of the PPSU hollow fiber surfaces was evaluated by AFM. It was found that the morphology of the PPSU fibers had both sponge-like and finger-like structures through different extrusion pressures and PPSU concentrations. The mean pore size and mean roughness for inner and outer surfaces were seen to be decreased with the increase of extrusion pressure at

In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.