Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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In this study, 25 clinical isolates of Proteus spp. were collected from urine, wounds and burns specimens from different hospitals in Baghdad city, all isolates were identified by using different bacteriological media, biochemical assays and Vitek-2 system. It was found that 15 (60%) isolates were identifies as Proteus mirabilis and 10 (40 %) isolates were Proteus vulgaris. The susceptibility of P. mirabilis and P. vulgaris isolates towards cefotaxime was (66.6 %) and (44.4 %) respectively; while the susceptibility of P. mirabilis and P. vulgaris isolates towards ceftazidime was (20%). Extended spectrum β-lactamses producing Proteus was (30.7 %). DNA of 10 isolates of P. mirabilis and 4 isolates of P. vulgaris were extracted and detecti
... Show MoreLet L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called s- closed submodule denoted by D ≤sc W, if D has no proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In this paper, we study modules which satisfies the ascending chain conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.
Our aim in this paper is to study the relationships between min-cs modules and some other known generalizations of cs-modules such as ECS-modules, P-extending modules and n-extending modules. Also we introduce and study the relationships between direct sum of mic-cs modules and mc-injectivity.
In previous our research, the concepts of visible submodules and fully visible modules were introduced, and then these two concepts were fuzzified to fuzzy visible submodules and fully fuzzy. The main goal of this paper is to study the relationships between fully fuzzy visible modules and some types of fuzzy modules such as semiprime, prime, quasi, divisible, F-regular, quasi injective, and duo fuzzy modules, where under certain conditions it has been proven that each fully fuzzy visible module is fuzzy duo. In addition, there are many various properties and important results obtained through this research, which have been illustrated. Also, fuzzy Artinian modules and fuzzy fully stable modules have been introduced, and we study the rel
... Show MoreLet R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXïƒW for all fully invariant R-submodule X of M, implies XïƒW. M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.
The research is an article that teaches some classes of fully stable Banach - Å modules. By using Unital algebra studies the properties and characterizations of all classes of fully stable Banach - Å modules. All the results are existing, and they've been listed to complete the requested information.
The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl
... Show MoreCollaborative learning in class‐based teaching presents a challenge for a tutor to ensure every group and individual student has the best learning experience. We present Group Tagging, a web application that supports reflection on collaborative, group‐based classroom activities. Group Tagging provides students with an opportunity to record important moments within the class‐based group work and enables reflection on and promotion of professional skills such as communication, collaboration and critical thinking. After class, students use the tagged clips to create short videos showcasing their group work activities, which can later be reviewed by the teacher. We report on a deployment of Group Tagging in an undergraduate Computing Scie
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