小阶非约环及其极大图

Q4 Mathematics
Arti Sharma, A. Gaur
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引用次数: 0

摘要

设$R$是一个具有非零恒等式的交换环。设$Gamma(R)$表示与R的非单位元素相对应的最大图,即$Gamma。在本文中,我们研究了对于给定的正整数$n$,是否存在具有$n$非单位的非约简环$R$?对于$n-leq100$,不可降分解环的完整列表$R=prod_{i=1}^{k}R_i给出了具有n个非单位的局部组成环$R_i$的基数。我们还证明了$n$,$(1leq n leq 7500)$,$|Center(Gamma(R)
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Non-reduced rings of small order and their maximal graph
Let $R$ be a commutative ring with nonzero identity. Let $Gamma(R)$ denotes the maximal graph corresponding to the non-unit elements of R, that is, $Gamma(R)$is a graph with vertices the non-unit elements of $R$, where two distinctvertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$containing both. In this paper, we investigate that for a given positive integer $n$, is there a non-reduced ring $R$ with $n$ non-units? For $n leq 100$, a complete list of non-reduced decomposable rings $R = prod_{i=1}^{k}R_i$ (up to cardinalities of constituent local rings $R_i$'s) with n non-units is given. We also show that for which $n$, $(1leq n leq 7500)$, $|Center(Gamma(R))|$ attains the bounds in the inequality $1leq |Center(Gamma(R))|leq n$ and for which $n$, $(2leq nleq 100)$, $|Center(Gamma(R))|$ attains the value between the bounds
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来源期刊
Journal of Algebra and Related Topics
Journal of Algebra and Related Topics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
0.60
自引率
0.00%
发文量
0
审稿时长
16 weeks
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