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.

     The present study includes a theoretical treatment to derive the general equations of pumping threshold power ( ), laser output power (P_out), and laser device efficiency (ƞ) of the element-doped thin-disk laser (Yb³⁺) with a quasi-three-level pumping scheme in the continuous wave mode at a temperature of (299K^°). In this study, the host crystals (YAG) were selected as typical examples of this laser design in a Gaussian transverse mode. The numerical solution of these equations was made using Matlab software by selecting the basic parameters from the recently published scientific articles for the laser design of these crystal hosts. According to this simulation, this article studied the effect o

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .

The main purpose of this paper is to show that zero symmetric prime near-rings, satisfying certain identities on n-derivations, are commutative rings.

      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 res

      As a new technology, blockchain provides the necessary capabilities to assure data integrity and data security through encryption. Mostly, all existing algorithms that provide security rely on the process of discovering a suitable key. Hence, key generation is considered the core of powerful encryption. This paper uses Zernike moment and Mersenne prime numbers to generate strong prime numbers by extracting the features from biometrics (speech). This proposed system sends these unique and strong prime numbers to the RSA algorithm to generate the keys. These keys represent a public address and a private key in a cryptocurrency wallet that is used to encrypt transactions. The benefit of this work is that it provides a high degree

Our active aim in this paper is to prove the following Let Ŕ be a ring having an
idempotent element e(e  0,e 1) . Suppose that R is a subring of Ŕ which
satisfies:
(i) eR  R and Re  R .
(ii) xR  0 implies x  0 .
(iii ) eRx  0 implies x  0( and hence Rx  0 implies x  0) .
(iv) exeR(1 e)  0 implies exe  0 .
If D is a derivable map of R satisfying D(R )  R ;i, j 1,2. ij ij Then D is
additive. This extend Daif's result to the case R need not contain any non-zero
idempotent element.

The main purpose of this work is to generalize Daif's result by introduceing the concept of Jordan (α β permuting 3-derivation on Lie ideal and generalize these result by introducing the concept of generalized Jordan (α β permuting 3-derivation 

In the current paper, we study the structure of Jordan ideals of a 3-prime near-ring which satisfies some algebraic identities involving left generalized derivations and right centralizers. The limitations imposed in the hypothesis were justified by examples.

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed