A new infinite family of $\sigma$-elementary rings

Autor:	Swartz, Eric, Werner, Nicholas J.
Rok vydání:	2022
Předmět:	Mathematics - Rings and Algebras Mathematics - Combinatorics 16P10 05E16
Druh dokumentu:	Working Paper
Popis:	A cover of an associative (not necessarily commutative nor unital) ring $R$ is a collection of proper subrings of $R$ whose set-theoretic union equals $R$. If such a cover exists, then the covering number $\sigma(R)$ of $R$ is the cardinality of a minimal cover, and a ring $R$ is called $\sigma$-elementary if $\sigma(R) < \sigma(R/I)$ for every nonzero two-sided ideal $I$ of $R$. In this paper, we provide the first examples of $\sigma$-elementary rings $R$ that have nontrivial Jacobson radical $J$ with $R/J$ noncommutative, and we determine the covering numbers of these rings. Comment: The content of the earlier paper "The covering numbers of rings" (arXiv:2112.01667) has been split into two parts. This article contains one part, and the updated version of arXiv:2112.01667 contains the rest
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.10313 Zobrazit plný text záznamu View this record from Arxiv