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Noetherian Properties and Growth of some Associative Algebras

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Effective Methods in Algebraic Geometry

Part of the book series: Progress in Mathematics ((PM,volume 94))

Abstract

We consider finitely generated associative algebras over a fixed K of arbitrary characteristic. For such an algebra A we impose some structural restrictions (we call A strictly ordered). We are interested in the implication of strict order on A for its noetherian properties and type of growth. In particular, we prove that if A is a graded standard finitely presented strictly ordered algebra, then A is right (left) noetherian if and only if A has polynomial growth. In this case A is almost commutative. It follows from this that the conjecture we made in [9] is true.

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Gateva-Ivanova, T. (1991). Noetherian Properties and Growth of some Associative Algebras. In: Mora, T., Traverso, C. (eds) Effective Methods in Algebraic Geometry. Progress in Mathematics, vol 94. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0441-1_9

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  • DOI: https://doi.org/10.1007/978-1-4612-0441-1_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6761-4

  • Online ISBN: 978-1-4612-0441-1

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