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pro vyhledávání: '"16Z05"'
Terwilliger algebras are finite-dimensional semisimple algebras that were first introduced by Paul Terwilliger in 1992 in studies of association schemes and distance-regular graphs. The Terwilliger algebras of the conjugacy class association schemes
Externí odkaz:
http://arxiv.org/abs/2411.08803
Autor:
Kuroki, Ryota
We give a constructive counterpart of the theorem of Andrunakievi\v{c} and Rjabuhin, which states that every reduced ring is a subdirect product of domains. As an application, we extract a constructive proof of the fact that every ring $A$ satisfying
Externí odkaz:
http://arxiv.org/abs/2408.09222
Let $K$ be a number field, let $A$ be a finite-dimensional semisimple $K$-algebra, and let $\Lambda$ be an $\mathcal{O}_{K}$-order in $A$. We give practical algorithms that determine whether or not $\Lambda$ has stably free cancellation (SFC). As an
Externí odkaz:
http://arxiv.org/abs/2407.02294
Autor:
Kreuzer, Martin, Walsh, Florian
Publikováno v:
journal of Groups, complexity, cryptology, Volume 16, Issue 1 (July 31, 2024) gcc:13875
For a commutative finite $\mathbb{Z}$-algebra, i.e., for a commutative ring $R$ whose additive group is finitely generated, it is known that the group of units of $R$ is finitely generated, as well. Our main results are algorithms to compute generato
Externí odkaz:
http://arxiv.org/abs/2405.07002
The aim of this article is to solve the system $XA=Y$ where $A=(a_{ij})\in M_{m\times n}(S)$, $Y\in S^{m}$ and $X$ is an unknown vector of size $n$, being $S$ an additively idempotent semiring. If the system has solutions then we completely character
Externí odkaz:
http://arxiv.org/abs/2404.03294
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology, which can be
Externí odkaz:
http://arxiv.org/abs/2404.02536
Let $\mathbb{F}_q$ be the finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(\gamma,\Delta)$-cyclic codes over a class of finite commutative non-chain rings $\mathscr{R}_{q,s}=\mathbb{F}_q[v_1,
Externí odkaz:
http://arxiv.org/abs/2404.01904
Autor:
Rathee, Nishant
Rota--Baxter operators over groups have been recently defined in \cite{LHY2021}, and they share a close connection with skew braces, as demonstrated in \cite{VV2022}. In this paper, we classify all Rota--Baxter operators of weight 1 over the Heisenbe
Externí odkaz:
http://arxiv.org/abs/2402.15428
Autor:
Brandenburg, Martin
A classical theorem by Jacobson says that a ring in which every element $x$ satisfies the equation $x^n=x$ for some $n>1$ is commutative. According to Birkhoff's Completeness Theorem, if $n$ is fixed, there must be an equational proof of this theorem
Externí odkaz:
http://arxiv.org/abs/2310.05301
Autor:
Buring, Ricardo, Kiselev, Arthemy V.
Publikováno v:
Journal of Physics: Conference Series, Vol.2667 (2023), Paper 012080, pp.1--8
The formula $\star$ mod $\bar{o}(\hbar^k)$ of Kontsevich's star-product with harmonic propagators was known in full at $\hbar^{k\leqslant 6}$ since 2018 for generic Poisson brackets, and since 2022 also at $k=7$ for affine brackets. We discover that
Externí odkaz:
http://arxiv.org/abs/2309.16664