We prove the Zariski dense orbit conjecture in positive characteristic for endomorphisms of G a N defined over F p ‾ .

We construct new families of elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the sameway asGallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Our construction is based on reducingQ-curves—curves over quadratic number fields without complex multiplication, butwith isogenies to their ...

Based on an embedding formula of the CAR algebra into the Cuntz algebra O2p , properties of the CAR algebra are studied in detail by restricting those of the Cuntz algebra. Various ∗-endomorphisms of the Cuntz algebra are explicitly constructed, and transcribed into those of the CAR algebra. In particular, a set of ∗-endomorphisms of the CAR algebra into its even subalgebra are constructed. Acc...

We construct new families of elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Our construction is based on reducing Q-curves—curves over quadratic number fields without complex multiplication, but with isogenies to th...

Let R be a regular local ring, and let A = R/(x), where x is any nonunit of R. We prove that every minimal free resolution of a finitely generated A -module becomes periodic of period 1 or 2 after at most dim A steps, and we examine generalizations and extensions of this for complete intersections. Our theorems follow from the properties of certain universally defined endomorphisms of complexes...

Abstract In this paper, we introduce an AEC framework for studying fields with commuting automorphisms. Fields automorphisms are closely related to difference fields. Some authors define a ring (or field) as together several endomorphisms, while others only study one endomorphism. Z. Chatzidakis and E. Hrushovski have studied in depth the model theory of ACFA, companion automorphism. Our genera...

We study $$(\sigma ,\tau )$$ -derivations of a group ring RG where G is with center having finite index in and R semiprime 1 such that either has no torsion elements or if p-torsion elements, then p does not divide the order let $$\sigma $$ be R-linear endomorphisms fixing pointwise. generalize Main Theorem 1.1 Chaudhuri (Comm Algebra 47(9): 3800–3807, 2019) prove there $$T\supset R$$ $$\mat...

We classify endomorphisms of the plane that preserve a pencil of curves.

We prove that any affine algebraic monoid can be obtained as the endomorphisms’ monoid of a finite-dimensional (nonassociative) algebra.