منابع مشابه
Annihilating polynomials for quadratic forms
This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field. 1991 A.M.S. Subject Classification : 11E81, 12F10, 19A22
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Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either E...
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Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where $mathbb{P}(R)$ is...
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Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...
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We consider pairs of n × n commuting matrices over an algebraically closed field F . For n, a, b (all at least 2) let V(n, a, b) be the variety of all pairs (A,B) of commuting nilpotent matrices such that AB = BA = A = B = 0. In [14] Schröer classified the irreducible components of V(n, a, b) and thus answered a question stated by Kraft [9, p. 201] (see also [3] and [10]). If μ = (μ1, μ2, . . ....
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2003
ISSN: 1246-7405
DOI: 10.5802/jtnb.390