10 papers
Sums of units in finite rings and applications to Cayley graphs
Ján MináÄ, Tung T. Nguyen, Nguyen Duy Tân
The question of whether a ring is additively generated by its units has been studied from several perspectives in ring theory and algebraic graph theory. In this paper, we investig…
Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
Arthur S. Powanwe, Luisa H. B. Liboni, Anif N. Shikder +7
We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption…
On the arithmetic of the join rings over finite fields
Sunil K. Chebolu, Jonathan Merzel, Ján MinÃ¡Ä +3
Given a collection of finite groups and a ring , we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1,…
The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one
Sunil K. Chebolu, Ján MináÄ, Cihan Okay +2
The famous Bloch--Kato conjecture implies that for a field containing a primitive th root of unity, the cohomology ring of the absolute Galois group of with $\math…
Maximal -extensions of Pythagorean fields and Right Angled Artin Groups
Oussama Hamza, Christian Maire, Ján MinÃ¡Ä +1
In this paper, we describe minimal presentations of maximal pro- quotients of absolute Galois groups of formally real Pythagorean fields of finite type. For this purpose, we int…
On the gcd graphs over polynomial rings
Ján MináÄ, Tung T. Nguyen, Nguyen Duy Tân
Gcd-graphs over the ring of integers modulo are a natural generalization of unitary Cayley graphs. The study of these graphs has foundations in various mathematical fields, inc…