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The Gelfand-Kirillov dimension of a tensor product

✍ Scribed by Robert B. Warfield

Publisher
Springer-Verlag
Year
1984
Tongue
French
Weight
364 KB
Volume
185
Category
Article
ISSN
0025-5874

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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