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pro vyhledávání: '"polynomial identities"'
We study algebras satisfying a two-term multilinear identity, namely one of the form $x_1\cdots x_n=qx_{\sigma(1)}\cdots x_{\sigma(n)}$, where $q$ is a parameter from the base field. We show that such algebras with $q=1$ and $\sigma$ not fixing~1 or~
Externí odkaz:
http://arxiv.org/abs/2407.09666
We give an affirmative answer to the open question posed in [34]: are the operated Lie polynomial identities corresponding to new operators on associative algebras in [7] Grobner-Shirshov, respectively?
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2404.13894
Publikováno v:
Communications in Mathematics, Volume 33 (2025), Issue 1 (March 27, 2024) cm:13107
In this paper we investigate weak polynomial identities for the Weyl algebra $\mathsf{A}_1$ over an infinite field of arbitrary characteristic. Namely, we describe weak polynomial identities of the minimal degree, which is three, and of degrees 4 and
Externí odkaz:
http://arxiv.org/abs/2402.14799