منابع مشابه
Noetherian Hopf Algebras
This short survey article reviews our current state of understanding of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed. To the memory of my teacher and friend Brian Hartley
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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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Let k be an uncountable algebraically closed field and let A be a countably generated left Noetherian k-algebra. Then we show that A⊗k K is left Noetherian for any field extension K of k. We conclude that all subfields of the quotient division algebra of a countably generated left Noetherian domain over k are finitely generated extensions of k. We give examples which show that A⊗k K need not re...
متن کاملNoetherian semigroup algebras and prime maximal orders
Let S be a semigroup and K be a field. A K-space K[S], with basis S and with multiplication extending, in a natural way, the operation on S, is called a semigroup algebra. It remains an open problem to characterize semigroup algebras that are a prime Noetherian maximal order. In this thesis, we give an answer to the problem for a large class of cancellative semigroups and we illustrate these re...
متن کاملOn Simplicial Commutative Algebras with Noetherian Homotopy
In this paper, we introduce a strategy for studying simplicial commutative algebras over general commutative rings R. Given such a simplicial algebra A, this strategy involves replacing A with a connected simplicial commutative k(℘)-algebra A(℘), for each ℘ ∈ Spec(π0A), which we call the connected component of A at ℘. These components retain most of the André-Quillen homology of A when the coef...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2012
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-15219