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Gelfand-Kirillov dimensions of a tensor product

✍ Scribed by J. Krempa; J. Okniński


Publisher
Springer-Verlag
Year
1987
Tongue
French
Weight
467 KB
Volume
194
Category
Article
ISSN
0025-5874

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Gelfand-Kirillov Dimension of Noetherian
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It is shown that for certain classes of semigroup algebras \(K[S]\), including right noetherian algebras, the Gelfand-Kirillov dimension is finite whenever it is finite on all cancellative subsemigroups of \(S\). Moreover, the dimension of the algebra modulo the prime radical is then an integer. A d

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We prove that any multi-filtered algebra with semi-commutative associated graded algebra can be endowed with a locally finite filtration keeping up the semi-commutativity of the associated graded algebra. As consequences, we obtain that Gelfand-Kirillov dimension is exact for finitely generated modu