Multilinear Polynomial Identities Under the Action of Generalized Skew Derivations

On σ -Twisted Functional Identities and Elementary Operators Over Division Rings

Homological finiteness of principal series representations of GL n ( R )

Commuting with Higher Centralizers on Prime Rings

The main purpose of this paper is studied the commuting on prime ring by using higher left (right) centralizers we have obtained several results that ensure a ring becomes commutative as assume 𝒥≠{0}an ideal of E. If E admits a higher left (right) centralizers 𝜅𝑛= (𝜅𝑖)𝑖∈𝑁s.t.𝜅𝑛(𝓅𝜈)–𝜅𝑛−1(𝓅𝜈)∈𝒵(E ) or 𝜅𝑛(𝓅𝜈) +𝜅𝑛−1(𝓅𝜈)∈𝒵(...

General linear and Steinberg groups over the Leavitt algebra $L_{\mathbb F_2}(1,2)$

Let $R=L_{\F_2}(1,2)$. We prove that $\GL_r(R)$ is integrally acyclic for every $r\geq1$ and that the canonical map $\St_r(R)\to\GL_r(R)$ is an isomorphism for every $r\geq3$. The unit group $R^\times$ is finitely presented, and we describe an explicit finite presentation. The homology calculation uses leaf coordinates...

An explicit family of twists of the Carlitz module with unbounded analytic rank

Grishkov and Logachev have asked (Problem 1.4 of their recent survey) whether, for a fixed finite field F_q, the analytic ranks of the twists of the Carlitz module are bounded. We answer this in the negative for every q>= 3. For q = p^s and n>= 1 put P_{q,n} = (theta^(q^n) - theta)^(q-2). We show that the directed grap...

IRREDUCIBILITY OF POLYNOMIALS WITH COEFFICIENTS IN A POSITIVE ARITHMETIC PROGRESSION