Let R be any ring with identity, and let M be a unitary left R-module. A submodule K of M is called generalized coessential submodule of N in M, if Rad( ). A module M is called generalized hollow-lifting module, if every submodule N of M with is a hollow module, has a generalized coessential submodule of N in M that is a direct summand of M. In this paper, we study some properties of this type of modules.
The main aim of this paper is to study the application of Weyl module resolution in the case of two rows, which will be specified in the skew- partition (6, 6)/(1,1) and (6,6)/(1,0), by using the homological Weyl (i.e. the contracting homotopy and place polarization).
The aim of this work is to survey the two rows resolution of Weyl module and locate the terms and the exactness of the Weyl Resolution in the case of skew-shape (8,6)/(2,1).
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The aim of this work is to study the application of Weyl module resolution in the case of two rows, which will be specified in the partition (7, 6) and skew- partition (7,6)/(1,0) by using the homological Weyl (i.e. the contracting homotopy and place polarization).
The purpose of this paper is to study the application of Weyl module’s resolution in the case of two rows which will be specified in the partitions (7, 7) and (7, 7) / (1, 0), using the homological Weyl (i.e. the contracting homotopy and place polarization).
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Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
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The question asked by all researchers is when solar panels will replace the national grid, especially in the domestic sector. In this study, a rooftop stand-alone solar electric system is designed to provide all the electrical power to a house in Baghdad-Iraq, using a (How to design PV system) simulation program. The feasibility of this system compared to the performance of the national electric grid and the system of private diesel generators is determined. The proposed solar system capacity is (25 kW), and the space required and the energy payback time are (360 m2 and 7.82 years), respectively. By using the current system, the net CO2 mitigation amount is 499,518.2 tons for 30-year. The kilowatt-hour cost
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Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.
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This paper aims to define and study new separation axioms based on the b-open sets in topological ordered spaces, namely strong - -ordered spaces ( ). These new separation axioms are lying between strong -ordered spaces and - - spaces ( ). The implications of these new separation axioms among themselves and other existing types are studied, giving several examples and counterexamples. Also, several properties of these spaces are investigated; for example, we show that the property of strong - -ordered spaces ( ) is an inherited property under open subspaces.
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Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between prime submodules of a given module and the extension of prime submodules. The relations between prime submodules of two given modules and the prime submodules in the direct product of their quotient module are studied and investigated.