This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.
Background: Saliva is a specific bio-fluid with important biomarkers. Analyzing any alternation in these markers could give valuable information, in relation to oral health status parameters. The aim of this study was to investigate the level of α -amylase in unstimulated whole saliva of healthy, primary school children in relation to some oral health parameters. Materials and Methods: A questionnaires consisted of demography and medical histories of participants were filled by children families. Saliva samples were collected for 5- minutes between 9:00 -11:00 AM from 114 healthy students aged 6-13 years, divided into four age groups. Flow- rate, Plaque and Gingival Index were assessed and dentition status was investigated by DMFT/dmft
... Show MoreBackground: Beta-thalassemia major is the most common monogenic known disorder in the Middle East, characterized by anomalies in the synthesis of the beta chains of hemoglobin resulting in variable phenotypes ranging from severe anemia to clinically asymptomatic Individuals. This study aimed to evaluate salivary flow rate and salivary IgA in β-thalassemia major patients. Since many oral and systemic conditions manifest themselves as changes in the flow and composition of saliva the dental practitioner is advised to remain up-to-date with this issue. Materials and methods: The study samples consist of (60) subjects, patients group composed of (30) patients with β –thalassemia major, age rang (5-23) years and (30) healthy locking
... Show MoreLet R be an associative ring. In this paper we present the definition of (s,t)- Strongly derivation pair and Jordan (s,t)- strongly derivation pair on a ring R, and study the relation between them. Also, we study prime rings, semiprime rings, and rings that have commutator left nonzero divisior with (s,t)- strongly derivation pair, to obtain a (s,t)- derivation. Where s,t: R®R are two mappings of R.
In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule of an -module is called an approximaitly prime submodule of (for short app-prime submodule), if when ever , where , , implies that either or . So, an ideal of a ring is called app-prime ideal of if is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.
Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.
Let ℛ be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z+, either rnℵ=0 or rnℵ=rℵ.
In this work, we introduce the concept of semisecond submodule and confer numerous properties concerning with this notion. Also we study semisecond modules as a popularization of second modules, where an ℛ-module ℬ is called semisecond, if ℬ is semisecond submodul of ℬ.
In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise Lindelöf and locally Lindelöf topological spaces, which are generalizations of will-known concepts: Lindelöf topological space (1) "A topological space X is called a Lindelöf space if for every open cover of X has a countable subcover" and locally Lindelöf topological space (1) "A topological space X is called a locally Lindelöf space if for every point x in X, there exist a nbd U of x such that the closure of U in X is Lindelöf space". Either the new concepts are: "A fibrewise topological space X over B is called a fibrewise Lindelöf if the projection function p : X→B is Lindelöf" and "The fibrewise topological space X over B
... Show MoreBackground: Invasion in oral cancer involves alterations in cell-cell and cell-matrix interactions that accompanied by loss of cell adhesion. Catenins stabilize cellular adherence junctions by binding to E-cadherin, which further mediates cell-cell adhesion and regulates proliferation and differentiation of epithelial cells. The Wnt/β-catenin pathway is one of the major signaling pathways in cell proliferation, oncogenesis, and epithelial-mesenchymal transition. Aims of the study: to detect immunohistochemical distribution pattern and different subcellular localization of β-catenin in oral squamous cell carcinoma and relate such expression to Bryne’s invasive grading system. Materials and Methods: This study included 30 paraffi
... Show MoreLet R be a commutative ring with unity and let M be a left R-module. We define a proper submodule N of M to be a weakly prime if whenever r  R, x  M, 0  r x  N implies x  N or r  (N:M). In fact this concept is a generalization of the concept weakly prime ideal, where a proper ideal P of R is called a weakly prime, if for all a, b  R, 0  a b  P implies a  P or b  P. Various properties of weakly prime submodules are considered.
In this paper, new concepts which are called: left derivations and generalized left derivations in nearrings have been defined. Furthermore, the commutativity of the 3-prime near-ring which involves some
algebraic identities on generalized left derivation has been studied.