We continue the development of the theory of higher-genus Möbius periodicity that was studied in Part I for odd characteristic, now treating asymptotic questions and the case of characteristic 2. The extra difficulties in characteristic 2 are overcome via rigid geometry in characteristic 0. The results on Möbius periodicity in any positive characteristic are used to incorporate a correction fac...

We prove some theorems in the setting of a 3-prime near-ring admitting a suitably constrained generalized derivation, thereby extending some known results on derivations. Moreover, we give an example proving that the hypothesis of 3-primeness is necessary.

For a ring endomorphism α and an α-derivation δ, we introduce α-compatible ideals which are a generalization of α-rigid ideals and study the connections of the prime radical and the upper nil radical of R with the prime radical and the upper nil radical of the Ore extension R[x;α, δ] and the skew power series R[[x;α]]. As a consequence we obtain a generalization of Hong, Kwak and Rizvi, 2005.

The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some...

A classical conjecture predicts how often a polynomial in Z[T ] takes prime values. The natural analogous conjecture for prime values of a polynomial f(T ) ∈ κ[u][T ], where κ is a finite field, is false. The conjecture over κ[u] was modified in earlier work by introducing a correction factor that encodes unexpected periodicity of the Möbius function at the values of f on κ[u] when f ∈ κ[u][T ]...

We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions f...

Recall that a commutative ring R is said to be a pseudo-valuation ring if every prime ideal of R is strongly prime. We define a completely pseudovaluation ring. Let R be a ring (not necessarily commutative). We say that R is a completely pseudo-valuation ring if every prime ideal of R is completely prime. With this we prove that if R is a commutative Noetherian ring, which is also an algebra ov...

For k a field of arbitrary characteristic, and R a k-algebra, we show that the PI degree of an iterated skew polynomial ring R[x1; τ1, δ1] · · · [xn; τn, δn] agrees with the PI degree of R[x1; τ1] · · · [xn; τn] when each (τi, δi) satisfies a qi-skew relation for qi ∈ k and extends to a higher qi-skew τi-derivation. We confirm the quantum Gel’fand-Kirillov conjecture for various quantized coord...