R. Sharma

activity

20172025

collaborators

9 papers

math.NT2025

The Exact Enumeration of $4$ -nomial and $5$ -nomial Multiples of the Product of Primitive Polynomials over GF(2)

Soniya Takshak, Rajendra Kumar Sharma

Linear feedback shift registers (LFSRs) are used to generate secret keys in stream cipher cryptosystems. There are different kinds of key-stream generators like filter generators,…

math.NT2024

Twisted Derivations in Algebraic Number Fields

Praveen Manju, Rajendra Kumar Sharma

Let $A$ be a commutative ring with unity and $B = A [θ]$ be an integral extension of $A$ . Assume that $B$ is an integral domain with quotient field $K$ and $E$ is…

math.NT2024

$(σ, τ)$ -Derivations of Number Rings with Coding Theory Applications

Praveen Manju, Rajendra Kumar Sharma

In this article, we study $(σ, τ)$ -derivations of number rings by considering them as commutative unital $Z$ -algebras. We begin by characterizing all $(σ, τ)$ -derivations…

math.RA2024

Inner and Outer Twisted Derivations of Cyclic Group Rings

Praveen Manju, Rajendra Kumar Sharma

In this article, we study twisted derivations of cyclic group rings. Let $R$ be a commutative ring with unity, $G$ be a finite cyclic group, and ( $σ, τ$ ) be a pair of $R$ -algebra e…

math.NT2024

$F_{q}$ -primitive points on varieties over finite fields

Soniya Takshak, Giorgos Kapetanakis, Rajendra Kumar Sharma

Let $r$ be a positive divisor of $q - 1$ and $f (x, y)$ a rational function of degree sum $d$ over $F_{q}$ with some restrictions, where the degree sum of a rational function $f…

math.RA2024

Inner and Outer Derivations of $F V_{8 n}$

Praveen Manju, Rajendra Kumar Sharma

Let $F$ be a field of characteristic $0$ or an odd rational prime $p$ . In this article, we give an explicit classification of all the inner and outer derivations of the gr…

math.RA2023

Derivations of Non-Commutative Group Algebras

Praveen Manju, Rajendra Kumar Sharma

In this article, we study the derivations of group algebras of some important groups, namely, dihedral ( $D_{2 n}$ ), Dicyclic ( $T_{4 n}$ ) and Semi-dihedral ( $S D_{8 n}$ ). First, we expl…

math.RA2023

$(σ, τ)$ -Derivations of Group Rings with Applications

Praveen Manju, Rajendra Kumar Sharma

Leo Creedon and Kieran Hughes in [18] studied derivations of a group ring $R G$ (of a group $G$ over a commutative unital ring $R$ ) in terms of generators and relators of group $G$ .…

math.NT2017

Primitive Element Pairs with One Prescribed Trace over a Finite Field

Anju Gupta, R. K. Sharma, Stephen D. Cohen

In this article, we establish a sufficient condition for the existence of a primitive element $α \in F_{q^{n}}$ such that the element $α + α^{- 1}$ is also a primitive element…

The Exact Enumeration of 4-nomial and 5-nomial Multiples of the Product of Primitive Polynomials over GF(2)

Twisted Derivations in Algebraic Number Fields

(σ,τ)-Derivations of Number Rings with Coding Theory Applications

Inner and Outer Twisted Derivations of Cyclic Group Rings

Fq​-primitive points on varieties over finite fields

Inner and Outer Derivations of FV8n​

Derivations of Non-Commutative Group Algebras

(σ,τ)-Derivations of Group Rings with Applications

Primitive Element Pairs with One Prescribed Trace over a Finite Field

The Exact Enumeration of $4$ -nomial and $5$ -nomial Multiples of the Product of Primitive Polynomials over GF(2)

$(σ, τ)$ -Derivations of Number Rings with Coding Theory Applications

$F_{q}$ -primitive points on varieties over finite fields

Inner and Outer Derivations of $F V_{8 n}$

$(σ, τ)$ -Derivations of Group Rings with Applications