In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.
The research aims to identify small and medium enterprises in accounting thought in terms of definition and concept, and this international financial reporting standard for small and medium-sized enterprises (SMEs) in the theoretical aspect. As for the practical aspect, the small and medium-sized enterprises standard has been applied to the financial statements of the company in question, the preparation of the opening entry on the date of the transition, the requirements of measurement and the accounting disclosure on the date following the application of the standard, and the preparation of the company's financial statements and the accompanying explanations according to the standard of small and medium-sized enterprises. The r
... Show MoreThis study was carried out at University of Baghdad - College of Agricultural Engineering Sciences - Research Station B during the autumn season 2019-2020, in order to evaluate the effect of Ozone and the foliar application of coconut water and moringa extract on the growth of broccoli plant grown in modified NFT film technology. A factorial experiment (2*5) was carried out within Nested Design with three replicates. The ozone treatment was distributed into the main plots which consisted of oxygen (O2) and ozone (O3). The foliar application of organic nutrients were distributed randomly within each replicate including five treatments, which were the control treatment (T0), Coconut water with two concentrations of 50 (T1) and 100 ml.
... Show MoreThis study was carried out at University of Baghdad - College of Agricultural Engineering Sciences - research station B during the fall season of 2019-2020, in order to evaluate the effect of Ozone enrichment and the foliar application of organic nutrient on nutrient and water use efficiency and fertilizer productivity of broccoli plant using the modified NFT film technology. A factorial experiment (2*5) was carried out within Nested Design with three replicates. The ozone treatment was distributed into the main plots which consisted of oxygen (O2) and ozone (O3). The foliar application of organic nutrients were distributed randomly within each replicate including five treatments, which were the control treatment (T0), Coconut wat
... Show MoreLet R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.
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.
Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as we discuss the relation between this concept and some other related concepts.
Let R be a commutative ring with identity, and M be unital (left) R-module. In this paper we introduce and study the concept of small semiprime submodules as a generalization of semiprime submodules. We investigate some basis properties of small semiprime submodules and give some characterizations of them, especially for (finitely generated faithful) multiplication modules.
Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.
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