Abstract Let R be a ring and let M an -module with $$S={\text {End}}_R(M)$$ S = End R ( M ) . The module is called quasi-dual Baer if for every fully invari...

Let R be a commutative ring with unity. And let E unitary R-module. This paper introduces the notion of 2-prime submodules as generalized concept ideal, where proper submodule H module F over is said to if , for r and x implies that or . we prove many properties this kind submodules, then only [N ] E, R. Also, non-zero multiplication module, [K: F] [H: every k such K. Furthermore, will study ba...

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...

Let $ {\mathcal{A}} be a unital \ast -algebra containing nontrivial projection. Under some mild conditions on , it is shown that map \Phi:{\mathcal{A}}\rightarrow{\mathcal{A}} nonlinear mixed Jordan triple * -derivation if and only \Phi an additive -derivation. In particular, we apply the above result to prime -algebras, von Neumann algebras with no central summands of type I_{1} factor algebra...

Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly a unital module over noncommutative ring with nonzero identity. This is new class between (weakly submodules) 2-absorbing submodules). Let R be identity $$1\ne 0$$ 1 ≠ 0 </mml:m...

Let φ(n) be the Euler-phi function, define φ0(n) = n and φk+1(n) = φ(φk(n)) for all k ≥ 0. We will determine an asymptotic formula for the set of integers n less than x for which φk(n) is y-smooth, conditionally on a weak form of the Elliott-Halberstam conjecture. 1.Introduction Integers without large prime factors, usually called smooth numbers, play a central role in several topics of number ...

Growth is one of the key processes in the dynamic of exploited resources, since it provides part of the information required for structured population models. Growth of mangrove cockle, Anadara tuberculosa was estimated through length-based methods (ELEFAN I y NSLCA) and using diverse shell length intervals (SLI). The variability of L(infinity), k and phi prime (phi') estimates and the effect o...

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, we introduce the concept $S$-prime submodules modules over rings. We investigate some properties class their homogeneous components. $N$ submodule such that $(N:_{R}M)\cap S=\emptyset $. say is \textit{a }$S$...

Let φ denote Euler’s phi function. For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n 6 x such that q ∤ φ(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the Hardy-Littlewood conjecture about counts of prime k-tuples and a conjecture o...

Throughout this note we will use the following standard notation from elementary number theory: p denotes a prime number, μ(n) is the Möbius function, φ(n) is the Euler phi function, ω(n) denotes the number of distinct prime divisors of n, and τ(n) is the number of positive integers which divide n. Also we use λ to denote Lebesgue measure on R/Z and dimX to denote the Hausdorff dimension of a s...