Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.
Let
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.
Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.
Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if for every submodule N of M, there exists a submodule K of N such that
he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga
... Show MoreThe concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.
This work represents the set of measurements of radon and thoron concentrations levels of soil-gas in Al-Kufa city in Iraq using electric Radon meter (RAD-7). Radon and thoron concentration were measured in soil-gas in 20 location for three depth of (50, 100 and 150) cm.
The results show that the emanation rate of radon and thoron gas varied from location to anther, depending on the geological formation. The Radon concentration in soil has been found to vary from (12775±400) Bq/m3 at 150 cm depth in location (sample K2) to (41.45±17) Bq/m3, for depth 150 cm in location (sample K20). The thoron concentration in soil has been found to vary from (198±8.5) Bq/m3 at 150 cm depth in location samples (K1 & K2) to undetected in the mos
In the present work, a set of indoor Radon concentration measurements was carried out in a number of rooms and buildings of Science College in the University of Mustansiriyah for the first time in Iraq using RAD-7 detector which is an active method for short time measuring compared with the passive method in solid state nuclear track detectors (SSNTD's). The results show that, the Radon concentrations values vary from 9.85±1.7 Bq.m-3 to 94.21±34.7 Bq.m-3 with an average value 53.64±26 Bq.m-3 which is lower than the recommended action level 200-300 Bq/m3 [ICRP, 2009].
The values of the annual effective dose (A.E.D) vary from 0.25 mSv/y to 2.38 mSv/y, with an average value 1.46±0.67 mSv/y which is lower than the recommended the rang