Ideal Structure of Leavitt Path Algebras with Coefficients in a Unital Commutative Ring
نویسندگان
چکیده
منابع مشابه
Weakly Noetherian Leavitt Path Algebras
We study row-finite Leavitt path algebras. We characterize the row-finite graphs E for which the Leavitt path algebra is weakly Noetherian. Our main result is that a Leavitt path algebra is weakly Noetherian if and only if there is ascending chain condition on the hereditary and saturated closures of the subsets of the vertices of the graph E.
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We start this paper by showing that the Leavitt path algebra of a (row-finite) graph is an algebra of quotients of the corresponding path algebra. The path algebra is semiprime if and only if whenever there is a path connecting two vertices, there is another one in the opposite direction. Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra is a Fountain-Gould algebra ...
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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...
متن کاملStructure of Leavitt path algebras of polynomial growth.
We determine the structure of Leavitt path algebras of polynomial growth and discuss their automorphisms and involutions.
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2015
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2014.946133