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Chains of Prime Ideals and Primitivity of ℤ -Graded Algebras

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Original languageEnglish
Pages (from-to)777-800
Number of pages24
JournalAlgebras and representation theory
Volume18
Issue number3
DOIs
Publication statusPublished - 1 Jun 2015

Abstract

In this paper we provide some results regarding affine, prime, Z-graded algebras R=⨁i∈ZRi generated by elements with degrees 1,−1 and 0, with R 0 finite-dimensional. The results are as follows. These algebras have a classical Krull dimension when they have quadratic growth. If R k ≠0 for almost all k then R is semiprimitive. If in addition R has GK dimension less than 3 then R is either primitive or PI. The tensor product of an arbitrary Brown-McCoy radical algebra of Gelfand Kirillov dimension less than three and any other algebra is Brown-McCoy radical.

ID: 23699340