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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
Autor:
Rubiano, Andrés, Reyes, Armando
We investigate the differential smoothness of a certain family of skew Poincar\'e-Birkhoff-Witt extensions.
Comment: 22 pages. arXiv admin note: substantial text overlap with arXiv:2409.10264, arXiv:2409.18947, arXiv:2408.16648, arXiv:2410.12701
Comment: 22 pages. arXiv admin note: substantial text overlap with arXiv:2409.10264, arXiv:2409.18947, arXiv:2408.16648, arXiv:2410.12701
Externí odkaz:
http://arxiv.org/abs/2410.13967
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
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
Autor:
Rubiano, Andrés, Reyes, Armando
In this paper, we investigate the differential smoothness of skew PBW extensions over commutative polynomial rings on one and two indeterminates.
Comment: 60 pages. arXiv admin note: text overlap with arXiv:2408.16648, arXiv:2409.10264; text ove
Comment: 60 pages. arXiv admin note: text overlap with arXiv:2408.16648, arXiv:2409.10264; text ove
Externí odkaz:
http://arxiv.org/abs/2409.18947
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
Comment: 32 pages. arXiv admin note: text overlap with arXiv:2408.16648
Externí odkaz:
http://arxiv.org/abs/2409.10264
Autor:
Rubiano, Andrés, Reyes, Armando
In this paper, we investigate the differential smoothness of bi-quadratic algebras on three generators with PBW basis.
Comment: 21 pages, 8 tables. arXiv admin note: text overlap with arXiv:1410.6587 by other authors
Comment: 21 pages, 8 tables. arXiv admin note: text overlap with arXiv:1410.6587 by other authors
Externí odkaz:
http://arxiv.org/abs/2408.16648
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
Autor:
Higuera, Sebastián, Reyes, Armando
In this paper, we study the uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials.
Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:2406.19935
Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:2406.19935
Externí odkaz:
http://arxiv.org/abs/2408.07073
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
Autor:
Higuera, Sebastián, Reyes, Armando
In this paper, we investigate the attached prime ideals of inverse polynomial modules over skew Ore polynomials.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2406.19935