Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of M is called St-closed in M, if N has no proper semi-essential extension in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K, then N = K. We investigate the main properties of this type of submodules, and discuss some results that are useful in our work. The class of semi-extending modules is a generalization to the notion of extending modules, where an R-module M is called semi-extending, if every submodule of M is a semi-essential in a direct summand of M. Various properties of semi-extending modules are obtained, and we study the relationships between this class of modules and other related concepts.
The study aims to examine the emotional innovation, constructive thinking, foresight, and meditation among university students. Besides, attempts to explore the relationship between emotional innovation and constructive thinking, the relationship between emotional innovation and foresight, and meditation, the relationship between constructive thinking and foresight, and meditation, finally, the relationship among emotional innovation, constructive thinking, foresight, and meditation of university students regarding the variables of gender and major. A total of (400) students were selected as a sample for the study. The results revealed that university students have a high level of emotional innovation that induce them to take positive ro
... Show MoreLonger Kurdish poetry translator important tributary of the tributaries of the Iraqi culture contemporary , and a wealth of knowledge rich experiences of an important segment of the Iraqi people , nicked culturally with the languages and cultures of the neighboring nations have , however, much of this potery under depends on the effect of the Arab form and complex , but suffered marginalization and loss as a result of repression by the governments of the country by successive throughout history , and tried to search that offers a vision on the theme of the place and its implications in the Kurdish poetry translator, through the election of a collection of poems and chisels, vertical than that of quantum poetic enormous , but thenature of
... Show MoreRainfall in Nigeria is highly dynamic and variable on a temporal and spatial scale. This has taken a more pronounced dimension due to climate change. In this study, Standard Precipitation Index (SPI) and Mann-Kendall test statistical tools were employed to analyze rainfall trends and patterns in Gombe metropolis between 1990 and 2020 and the ARIMA model was used for making the forecast for ten (10) years. Daily rainfall data of 31 years obtained from Nigerian Meteorological Agency, (NIMET) was used for the study. The daily rainfall data was subjected to several analyses. Standard precipitation index showed that alternation of wet and dry period conditions had been witnessed in the study area. The result obtained showed that there is an u
... Show MoreThe ground state proton, neutron and matter densities of exotic 11Be and 15C nuclei are studied by means of the TFSM and BCM. In TFSM, the calculations are based on using different model spaces for the core and the valence (halo) neutron. Besides single particle harmonic oscillator wave functions are employed with two different size parameters Bc and Bv. In BCM, the halo nucleus is considered as a composite projectile consisting of core and valence clusters bounded in a state of relative motion. The internal densities of the clusters are described by single particle Gaussian wave functions.
Elastic electron scattering proton f
... Show MoreTwelve compounds containing a sulphur- or oxygen-based heterocyclic core, 1,3- oxazole or 1,3-thiazole ring with hydroxy, methoxy and methyl terminal substituent, were synthesized and characterized. The molecular structures of these compounds were performed by elemental analysis and different spectroscopic tequniques. The liquid crystalline behaviors were studied by using hot-stage optical polarizing microscopy and differential scanning calorimetry. All compounds of 1,4- disubstituted benzene core with oxazole ring display liquid crystalline smectic A (SmA) mesophase. The compounds of 1,3- and 1,4-disubstituted benzene core with thiazole ring exhibit exclusively enantiotropic nematic liquid crystal phases.
The Albian Carbonate-clastic succession in the present study is represented by the Mauddud and Nahr Umr formations were deposited during the Albian stage within the Wasia Group More than 200 thin sections of cores and cuttings in addition to well logs data for Nahr Umr and Mauddud formations from 4 boreholes within two oil fields (Ba-4, Ba-8, Ns-2 and Ns-4) were used to interpret the different associations facies as well as the facies architectures to describe the sedimentary framework of the basin and development the petrophysical properties. Seven major microfacies were diagnosed in the carbonate succession of the Mauddud Formation, while the Nar Umr Formation includes five lithofacies; their grain types characteristic and deposit
... Show MoreEssential oils of eucalyptus leaves and clove buds were isolated and tested for their bioherbicidal potential on different annual weed species. Gas Chromatography-Mass Spectrophotometry analysis (GC-MS) identified thirteen compounds representing around 87.11% of the total isolated eucalyptus oil. The main constituent was 1,8-cineole, which accounted for 68.15% of the total identified compounds. As for clove oil, eleven compounds were identified, representing 90.03% of the total compounds. Eugenol was the dominant compound and accounted for 73.89%. The bioherbicidal efficacy of the two oils and their combinations by three concentrations (2.5, 5, and 10%) were tested on four weedy species, namely Chenopodium album, Raph
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