Om Prakash

collaborators

4 papers

math.NT2024

No proper generalized quadratic forms are universal over quadratic fields

Ondřej Chwiedziuk, Matěj Doležálek, Simona Hlavinková +5

We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be…

math.RA2023

Additivity of multiplicative (generalized) skew semi-derivations on rings

Sk. Aziz, Arindam Ghosh, Om Prakash

In this paper, we introduce a new class of derivations that generalizes skew derivations and semi-derivations, and we call it ``skew semi-derivation". Further, we present a study o…

math.NT2023

Generalized Fruit Diophantine equation and Hyperelliptic curves

Om Prakash, Kalyan Chakraborty

We show the insolvability of the Diophantine equation $a x^{d} - y^{2} - z^{2} + x y z - b = 0$ in $Z$ for fixed $a$ and $b$ such that $a \equiv 1 (mod 12)$ and $b = 2^{d} a - 3$ , where $d$ is an…

math.RA2023

Some generalized Jordan maps on triangular rings force additivity

Sk Aziz, Arindam Ghosh, Om Prakash

In this paper, we show that a map $δ$ over a triangular ring $T$ satisfying $δ (ab + ba) = δ (a) b + a τ (b) + δ (b) a + b τ (a)$ , for all $a, b \in T$ and for some maps $τ$ over $…