The Brauer group of a commutative ring
نویسندگان
چکیده
منابع مشابه
Galois-azumaya Extensions and the Brauer-galois Group of a Commutative Ring
Introduction. Galois extensions of noncommutative rings were introduced in 1964 by Teruo Kanzaki [13]. These algebraic objects generalize to noncommutative rings the classical Galois extensions of fields and the Galois extensions of commutative rings due to Auslander and Goldman [1]. At the same time they also turn out to be fundamental examples of Hopf-Galois extensions; these were first consi...
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The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphlc image of a group ring RG for some finite group G. It is the purpose of ths article to continue an investigation of this group which was introduced in earler work as a natural gene=allzatlon of the Schur group of a field. We generalize certain facts pertaining to t...
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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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Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1960
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1960-0121392-6