Results 61 to 70 of about 39,950 (199)

Strongly Involution k-regular nil clean ring

NTU Journal of Pure Sciences
This article is about A-rings R, for which every element is a sum of an involution k-regular element and a nilpotent element, which commute with each other. These rings are called strongly involution k-regular nil-clean rings or SIKRNC rings.
Ali Shakir Mahmood, Zubaida Mohammed Ibraheem   +1 more
doaj   +1 more source

Reduced and irreducible simple algebraic extensions of commutative rings [PDF]

Mathematica Moravica, 2017
Let A be a commutative ring with identity and be an algebraic element over A. We give necessary and sufficient conditions under which the simple algebraic extension A[α] is without nilpotent or without idempotent elements.
Mihovski S.V.
doaj  

Uniform growth in small cancellation groups

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract An open question asks whether every group acting acylindrically on a hyperbolic space has uniform exponential growth. We prove that the class of groups of uniform uniform exponential growth acting acylindrically on a hyperbolic space is closed under taking certain geometric small cancellation quotients.
Xabier Legaspi, Markus Steenbock
wiley   +1 more source

A P‐adic class formula for Anderson t‐modules

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract In 2012, Taelman proved a class formula for L$L$‐series associated to Drinfeld Fq[θ]$\mathbb {F}_q[\theta]$‐modules and considered it as a function field analogue of the Birch and Swinnerton‐Dyer conjecture. Since then, Taelman's class formula has been generalized to the setting of Anderson t$t$‐modules.
Alexis Lucas
wiley   +1 more source

Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
wiley   +1 more source

On prime rings with commuting nilpotent elements [PDF]

Proceedings of the American Mathematical Society, 2009
An open question of Herstein asks whether a simple ring in which all nilpotent elements commute must have no nonzero nilpotent elements. The authors, addressing this question in the context of prime rings, show that a prime ring \(R\) with commuting nilpotent elements has no nonzero nilpotent elements if it satisfies one of the following conditions: (i)
Chebotar, M. A., Lee, P. H., Puczylowski, E. R.   +2 more
openaire   +2 more sources

Groups with conjugacy classes of coprime sizes

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract Suppose that x$x$, y$y$ are elements of a finite group G$G$ lying in conjugacy classes of coprime sizes. We prove that ⟨xG⟩∩⟨yG⟩$\langle x^G \rangle \cap \langle y^G \rangle$ is an abelian normal subgroup of G$G$ and, as a consequence, that if x$x$ and y$y$ are π$\pi$‐regular elements for some set of primes π$\pi$, then xGyG$x^G y^G$ is a π ...
R. D. Camina, A. Maróti, E. Pacifici, C. Parker, K. Rekvényi, J. Saunders, V. Sotomayor, G. Tracey, M. van Beek   +8 more
wiley   +1 more source

Rings in Which Every Element Is a Sum of a Nilpotent and Three 7-Potents

International Journal of Mathematics and Mathematical Sciences
In this article, we define and discuss strongly S3,7 nil-clean rings: every element in a ring is the sum of a nilpotent and three 7-potents that commute with each other.
Yanyuan Wang, Xinsong Yang
doaj   +1 more source

A note on commutativity of automorphisms

International Journal of Mathematics and Mathematical Sciences, 1998
Let α and β automorphisms of a ring satisfying the equation α+α−1=β+β−1. In this paper we prove some results where this equation itself implies the commutativity of α and β.
M. S. Samman, M. Anwar Chaudhry, A. B. Thaheem   +2 more
doaj   +1 more source

Linear Diophantine equations and conjugator length in 2‐step nilpotent groups

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract We establish upper bounds on the lengths of minimal conjugators in 2‐step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diophantine equations. We prove that in some cases these bounds are sharp.
M. R. Bridson, T. R. Riley
wiley   +1 more source