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: Recent studies suggest that chronic periodontitis (CP) and type2 diabetes mellitus (T2DM) are bidirectionally associated. Analysis of saliva as a mirror of oral and systemic health could allow identification of α amylase (α-Am) and albumin (A1) antioxidant system markers to assist in the diagnosis and monitoring of both diseases. The present study aims at comparing the clinical periodontal parameters in chronic periodontitis patients with poorly or well controlled Type 2Diabetes Mellitus, salivary α-Am, A1, flow rate (FR) and pH then correlate between biochemical, physical and clinical periodontal parameters of each study and control groups. Materials and Methods: 80 males, with an age range of (35-50) years were divide
... Show MoreOur 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.
Let 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.
Let S be an inverse semiring, and U be an ideal of S. In this paper, we introduce the concept of U-S Jordan homomorphism of inverse semirings, and extend the result of Herstein on Jordan homomorphisms in inverse semirings.
We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module over a commutative ring with identity as a generalization of a prime submodules and semi-prime submodules, also generalization of quasi-prime submodules and approximaitly prime submodules. Various basic properties of an approximaitly semi-prime submodules are discussed, where a proper submodule of an -module is called an approximaitly semi-prime submodule of , if whenever , where , and , implies that . Furthermore the behaviors of approximaitly semi-prime submodule in some classes of modules are studied. On the other hand several characterizations of this concept are
... Show MoreIn this article, the partially ordered relation is constructed in geodesic spaces by betweeness property, A monotone sequence is generated in the domain of monotone inward mapping, a monotone inward contraction mapping is a monotone Caristi inward mapping is proved, the general fixed points for such mapping is discussed and A mutlivalued version of these results is also introduced.
The purpose of this paper is to study a new class of fuzzy covering dimension functions, called fuzzy
Let 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.
Background: Crohn's disease (CD) is an immunological disorder associated with chronic inflammatory process of several unspecific regions of gastrointestinal tract but frequently detected in the terminal Ilium and proximal colon or both. This disease frequently presented with various oral manifestations as a consequence of inflammatory process of the disease, nutritional deficiency or medications side effects. Several therapeutic approaches have been developed for CD management that are targeting the inflammatory process and directed at controlling the host immune response. Immunosuppressants such as Azathioprine and anti-TNF α agents as well as the combination of them have been widely used as an effective therapeutic modality with a bett
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