Ore Extensions of Abelian Groups with Operators

Autor: Bäck, Per, Lundström, Patrik, Öinert, Johan, Richter, Johan

Given a set $A$ and an abelian group $B$ with operators in $A$, in the sense of Krull and Noether, we introduce the Ore group extension $B[x ; \delta_B , \sigma_B]$ as the additive group $B[x]$, with $A[x]$ as a set of operators. Here, the action of

Externí odkaz: http://arxiv.org/abs/2410.16761

Smooth Geometry of Diffusion Algebras

Autor: Rubiano, Andrés, Reyes, Armando

In this paper, we study the differential smoothness of diffusion algebras.
Comment: 32 pages. arXiv admin note: text overlap with arXiv:2409.18947, arXiv:2408.16648, arXiv:2409.10264

Externí odkaz: http://arxiv.org/abs/2410.12701

Smooth geometry of double extension regular algebras of type (14641)

Autor: Rubiano, Andrés, Reyes, Armando

In this paper, we prove that double extension regular algebras of type (14641) are not differentially smooth.
Comment: 32 pages. arXiv admin note: text overlap with arXiv:2408.16648

Externí odkaz: http://arxiv.org/abs/2409.10264

Bounded skew power series rings for inner $\sigma$-derivations

Autor: Jones, Adam, Woods, William

We define and explore the bounded skew power series ring $R^+[[x;\sigma,\delta]]$ defined over a complete, filtered, Noetherian prime ring $R$ with a commuting skew derivation $(\sigma,\delta)$. We establish precise criteria for when this ring is wel

Externí odkaz: http://arxiv.org/abs/2408.10545

$\sigma$-matching and interchangeable structures on certain associative algebras

Autor: Khrypchenko, Mykola

Publikováno v: Communications in Mathematics, Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar) (November 20, 2024) cm:13990

We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on some classes of associative algebras, including unital algebras, the semigroup algebras of rectangular bands, algebras with enough idempotents, free

Externí odkaz: http://arxiv.org/abs/2407.18734