Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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Abstract In this work we introduce the concept of approximately regular ring as generalizations of regular ring, and the sense of a Z- approximately regular module as generalizations of Z- regular module. We give many result about this concept.

This study was conducted for evaluating the cytotoxic effect of heat stable enterotoxin a (STa) produced by enterotoxigenic Escherichia coli on the proliferation of primary cancer cell cultures, obtained from tumor samples that were collected from (13) cancer patients and as follows: (five colon cancer patients, two bladder cancer patients, two breast cancer patients, two stomach cancer patients and two lung cancer patients), and on normal cell line (rat embryonic fibroblast / REF) (in vitro) with the use of different concentrations starting from (1) mg/ml and ending with (0.0002) mg/ml by making two fold serial dilutions by using the 96- well microtiter plate, and in comparison with negative (PBS) and positive (MMC, at concentration

      Let S be a commutative ring with identity, and A is an S-module. This paper introduced an important concept, namely strongly maximal submodule. Some properties and many results were proved as well as the behavior of that concept with its localization was studied and shown.

The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.

        Let R be a commutative ring with  identity . In this paper  we study  the concepts of  essentially quasi-invertible submodules and essentially  quasi-Dedekind modules  as  a generalization of  quasi-invertible submodules and quasi-Dedekind  modules  . Among the results that we obtain is the following : M  is an essentially  quasi-Dedekind  module if and only if M is aK-nonsingular module,where a module M is K-nonsingular if, for each  , Kerf ≤_e M   implies   f = 0 .