Papers by Dr. Asaad Hosain
Iraqi journal of science, Apr 30, 2024
Many researchers discussed distributive modules and their properties. In this work, the distribut... more Many researchers discussed distributive modules and their properties. In this work, the distributive property will be studied over semimodules. Some of the results obtained in homomorphisms of distributive modules are generalized. Some conditions were needed like concept subtractive, i-regular, k-regular, and k-cyclic, to get good results. The relationship between the distributive semimodule over the local semiring and the hollow semimodule was obtained, and the relationship between the distributive semimodule and the homomorphisms distributed over the intersection process or the inverse image distributed over the addition.
Journal of Kufa for Mathematics and Computer, Aug 30, 2023
This article explores the properties and theorems pertaining to subtractive and distributive semi... more This article explores the properties and theorems pertaining to subtractive and distributive semimodules. The focus is on understanding the relations between these characteristics and their implications within the context of semimodules. The investigated propositions establish conditions for distributivity in semimodules. It is shown that under certain circumstances, the preimages of subsemimodules under homomorphisms exhibit specific additive properties. Furthermore, the study introduced definitions and propositions related to supplements, principally supplemented semimodules and H-supplemented semimodules. The findings reveal the importance of supplements in understanding the structure and properties of semimodules, particularly in relation to their distributive nature.
Journal of Kufa for Mathematics and Computer, Aug 30, 2023
This work considers the construction of the concept of distributive property for semimodules. Som... more This work considers the construction of the concept of distributive property for semimodules. Some characterizations of this property, with some examples are given. Some conditions on semiring or semimodules (like subtractive, semisubtractive, cancellative, and k-cyclic) are required to obtain interesting results. The main results are: Any subsemimodule and factor semimodule of a distributive semimodule is distributive. Moreover, weakly distributive, is also, introduced and investigated. It is found that the semimodule is distributive if and only if each subsemimodule is weak distributive. Taking advantage of the supplemented concept to find some properties of distributive semimodule. Finally, the summand sum and summand intersection properties for distributive semimodules with some conditions are valid.
Baghdad Science Journal, Apr 20, 2023
The basis of this paper is to study the concept of almost projective semimodules as a generalizat... more The basis of this paper is to study the concept of almost projective semimodules as a generalization of projective semimodules. Some of its characteristics have been discussed, as well as some results have been generalized from projective semimodules.
Iraqi Journal of Science
The concept of semi-essential semimodule has been studied by many researchers. In this... more The concept of semi-essential semimodule has been studied by many researchers. In this paper, we will develop these results by setting appropriate conditions, and defining new properties, relating to our concept, for example (fully prime semimodule, fully essential semimodule and semi-complement subsemimodule) such that: if for each subsemimodule of -semimodule is prime, then is fully prime. If every semi-essential subsemimodule of -semimodule is essential then is fully essential. Finally, a prime subsemimodule of is called semi-relative intersection complement (briefly, semi-complement) of subsemimodule in , if , and whenever with is a prime subsemimodule in , , then . Furthermore, some results about the above concepts have been mentioned.
International journal of health sciences
A New generalization of injective semimodule has been presented in this working paper. An Ȑ-semim... more A New generalization of injective semimodule has been presented in this working paper. An Ȑ-semimodule Ӎ is called almost self-injective, if Ӎ is almost Ӎ-injective semimodule. Some properties of this notion have been presented. The relationship of this concept to some concepts has also been clarified as End (Ȑ) of indecomposable almost self-injective semimodules, Rad (Ȑ) also some related notions of it have been studied.
Journal of University of Babylon, 2019
Solid State Technology, 2020
π-injective modules over a ring have been studied by many authors. Quasi-continuous modules is an... more π-injective modules over a ring have been studied by many authors. Quasi-continuous modules is another name of this concept. In this work π-injective semimodule over a semiring will be introduced and investigated. If W is a semimodule over a semiring R then W is said to be π-injective if for any two subsemimodulesE1, E2 of W with E1∩E2=0, there existα, β ϵEnd(W) such that: i) α, β are idempotent. ii) α+β=1W. iii) E1 and E2 .
Journal of Physics: Conference Series, 2020
The aim of this action is a study and investigate “Von Neumann regular” semirings, some related c... more The aim of this action is a study and investigate “Von Neumann regular” semirings, some related concepts, e.g. reduced semirings; duo semiring, quasi-duo, and weakly duo semirings; regular, weakly regular and strongly regular semirings, also investigated. Some known results related to those concepts in rings were converted to semirings. Another aim of this paper is characterization Von Neumann Regular condition by the principal right ideal generated by an idempotent element.
Iraqi Journal of Science, 2020
In modules there is a relation between supplemented and π-projective semimodules. This relation w... more In modules there is a relation between supplemented and π-projective semimodules. This relation was introduced, explained and investigated by many authors. This research will firstly introduce a concept of "supplement subsemimodule" analogues to the case in modules: a subsemimodule Y of a semimodule W is said to be supplement of a subsemimodule X if it is minimal with the property X+Y=W. A subsemimodule Y is called a supplement subsemimodule if it is a supplement of some subsemimodule of W. Then, the concept of supplemented semimodule will be defined as follows: an S-semimodule W is said to be supplemented if every subsemimodule of W is a supplement. We also review other types of supplemented semimodules. Previously, the concept of π-projective semimodule was introduced. The main goal of the present study is to explain the relation between the two concepts, supplemented semimodule and π-projective semimodules, and prove these relations by many results.
2021 7th International Conference on Contemporary Information Technology and Mathematics (ICCITM), 2021
Themain aim of this research is to present and study several basic characteristics of the idea of... more Themain aim of this research is to present and study several basic characteristics of the idea of t-extending semimodules. The semimodule $F$ is said to be a t-extending semimodule if each t-closed sub-semimodule of $F$ is t-essential in a direct summand of $F$. Hence, the behavior of the t-extending semimodule is considered. In addition, the relationship between the t-essential (t-closed) and essential (closed) has been studied and investigated as well. Finally, in this work, there are a number of results related to the t-extending property, which is one of the generalizations of extending property, (every extending is t-extending, while the converse is not true).
Iraqi journal of science, Mar 30, 2022
The main aim of this research is to present and to study several basic characteristics of the ide... more The main aim of this research is to present and to study several basic characteristics of the idea of FI-extending semimodules. The semimodule is said to be an FI-extending semimodule if each fully invariant subsemimodule of is essential in direct summand of. The behavior of the FI-extending semimodule with respect to direct summands as well as the direct sum is considered. In addition, the relationship between the singularity and FI-extending semimodule has been studied and investigated. Finally extending propertywhich is stronger than FI extending, that has some results related to FI-extending and singularity is also investigated.
Iraqi Journal of Science
Let R be a ring with identity and Ą a left R-module. In this article, we introduce new general... more Let R be a ring with identity and Ą a left R-module. In this article, we introduce new generalizations of compressible and prime modules, namely s-compressible module and s-prime module. An R-module A is s-compressible if for any nonzero submodule B of A there exists a small f in HomR(A, B). An R-module A is s-prime if for any submodule B of A, annR (B) A is small in A. These concepts and related concepts are studied in as well as many results consist properties and characterizations are obtained.
Iraqi Journal of Science, 2022
Let A, and N are a semiring ,and a left A- semimodule, respectively. In this work we will... more Let A, and N are a semiring ,and a left A- semimodule, respectively. In this work we will discuss two cases: The direct summand of π-projective semi module is π-projective, while the direct sum of two π-projective semimodules in general is not π-projective . The details of the proof will be given. We will give a condition under which the direct sum of two π-projective semi modules is π-projective, as well as we also set conditions under which π-projective semi modules are projective.
Journal of Asian Scientific Research, 2014
The concept of full d-stability of modules was introduced by the authors in a previous paper. It ... more The concept of full d-stability of modules was introduced by the authors in a previous paper. It is stronger than the duo property. Although quasi-projectivity is not a necessary condition for full d-stability, it is inherent with this property in most of the known examples in such a way that it was difficult to give an example of a fully d-stable module which is not quasi-projective. This motivates the subject of this paper.
Journal of Physics: Conference Series
The objective of our research paper is to introduce as well as to study many essential properties... more The objective of our research paper is to introduce as well as to study many essential properties of the concept of extending semimodules. A semimodule S is named extending (CS) if every subsemimodule of S is essential in a direct summand of S. Therefore, extending semimodule behaviour with respect to direct sums and direct summands are examined. Moreover, studying some properties of these semimodules concepts, e.g., every direct summand of a CS-semimodule is a CS-semimodule. While the direct sum of extending semimodules is not necessarily extending.
Baghdad Science Journal
The fresh water green alga Chlorella vulgaris was selected to study its ability to degrade one of... more The fresh water green alga Chlorella vulgaris was selected to study its ability to degrade one of polycyclic aromatic hydrocarbon (PAHs)known is anthracene (ANT). ANT is widely used in artificial products such as wood preservatives; insecticides; dye and coating materials. This algae was cultivated in CH-10 medium under constant laboratory conditions and exposed to different concentrations (1, 3, and 5 mg/l) of anthracene for 3, 5, 7, 9 and 15 days, with the concentration of ANT measured by high performance liquid chromatographic analysis (HPLC). The results showed that C.vulgaris has high ability to reduce anthracene to 80% at 1mg/Lcon centration after 3 days and 100% after 5 days, while at 3 and 5 mg / L concentration, the highest percentages were 89% and 99%, respectively after 9 days, with the complete removal (100%) was achieved after 15 days. The results indicate that this alga(C. vulgaris) has high ability for remediation of ANT and yield not toxic compound to environment
Iraqi Journal of Science
In this paper, we study the class of prime semimodules and the related concepts, such as the clas... more In this paper, we study the class of prime semimodules and the related concepts, such as the class of semimodules, the class of Dedekind semidomains, the class of prime semimodules which is invariant subsemimodules of its injective hull, and the compressible semimodules. In order to make the work as complete as possible, we stated, and sometimes proved, some known results related to the above concepts.
Iraqi Journal of Science
The aim of this paper is to introduce the concept of Dedekind semimodules and study the related c... more The aim of this paper is to introduce the concept of Dedekind semimodules and study the related concepts, such as the class of semimodules, and Dedekind multiplication semimodules . And thus study the concept of the embedding of a semimodule in another semimodule.
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Papers by Dr. Asaad Hosain