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Examples in finite Gel'fand–Kirillov dimension

✍ Scribed by Jason P. Bell

Book ID
104140559
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
143 KB
Volume
263
Category
Article
ISSN
0021-8693

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✦ Synopsis

By modifying constructions of Beȋdar and Small we prove that for countably generated prime F -algebras of finite GK dimension there exists an affinization having finite GK dimension. Using this result we show: for any field there exists a prime affine algebra of GK dimension two that is neither primitive nor PI; for any countable field F there exists a prime affine F -algebra of GK dimension three that has non-nil Jacobson radical; for any countable field F there exists an affine primitive F -algebra of GK dimension at most four with center equal to a polynomial ring; for a countable field F there exists a primitive affine Jacobson F -algebra of GK dimension three that does not satisfy the Nullstellensatz.

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∗-Orderings and ∗-valuations on algebras
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✍ Murray Marshall 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 198 KB

The paper considers the real \* -spectrum of a ÿnitely generated algebra with involution over C of ÿnite Gelfand-Kirillov dimension. It is shown that for such an algebra the stability indices associated to the real \* -spectrum are bounded by the Gelfand-Kirillov dimension, as in the commutative cas