we investigate the classical h.~zassenhaus conjecture‎ ‎for integral group rings of alternating groups $a_9$ and $a_{10}$ of degree‎ ‎$9$ and $10$‎, ‎respectively‎. ‎as a consequence of our‎ ‎previous results we confirm the prime graph‎ ‎conjecture for integral group rings of $a_n$ for all $n leq 10$‎.

The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical holes. classical Lyapunov exponents corresponding nearly bound null geodesics control quasinormal ringing perturbed as it settles back down equilibrium, and they admit holographic interpretation in terms quantum Ruelle resonances microstate dual Kerr hole. Rec...

Let K[HKΘ] denote the Hecke–Kiselman algebra of a finite oriented graph Θ over an algebraically closed field K. All irreducible representations, and corresponding maximal ideals K[HKΘ], are characterized in case this satisfies polynomial identity. The latter condition corresponds to simple that can be expressed terms Θ. result shows surprising similarity classical results on representations sem...

One of the central problems of algebraic K-theory is to compute the K-groups KX of a scheme X. Since these groups are, by definition, the homotopy groups of a spectrum KX, it makes sense to analyze the homotopy-type of the spectrum, rather than just the disembodied homotopy groups. In addition to facilitating the computation of the K-groups themselves, knowledge of the spectrum KX can be applie...

In this paper, we study the relationships between graphs and prime spectrum of unitary commutative rings. It is shown that a graph G equipped with G-right topology satisfies some spectral properties. particular give necessarily sufficient condition to obtain graph.

We propose a quantum circuit that creates a pure state corresponding to the quantum superposition of all prime numbers less than 2, where n is the number of qubits of the register. This Prime state can be built using Grover’s algorithm, whose oracle is a quantum implementation of the classical Miller-Rabin primality test. The Prime state is highly entangled, and its entanglement measures encode...

For any field F , we give an example of a prime finitely generated F -algebra of GK dimension 2 for which GK dimension is not finitely partitive. For each m ∈ {0, 1, 2, 3, . . .}∪{∞}, we give an example of a prime finitely generated F -algebra having GK dimension 2 which has classical Krull dimension m; the algebra of GK dimension 2 which has infinite classical Krull dimension has the additiona...

We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. This result generalizes the classical theorem of Duistermaat-Guillemin for compact manifolds and the results of GuillopéZworski, Perry, and Guillarmou-Naud...