By Jan-Erik Roos

ISBN-10: 3540164537

ISBN-13: 9783540164531

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**Read Online or Download Algebra, Algebraic Topology and their Interactions: Proceedings of a Conference held in Stockholm, Aug. 3 - 13, 1983, and later developments PDF**

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**Extra resources for Algebra, Algebraic Topology and their Interactions: Proceedings of a Conference held in Stockholm, Aug. 3 - 13, 1983, and later developments **

**Sample text**

This again follows by an explicit computation in a few eases. All the operations on ~ we have discussed so far have the property that if we start with rational Hilbert series,we end up with a rational series. In theorem 5 we discuss some operations for which this is not the case. In each of the constructions of theorem 5 , we obtain a Hilbert series which equals a rational function times a transcendental power of the original series. ,UM } . ,t N} G(z) = n=~0g n z n 6 ~ " there exist D, E E ~ I such that oo (a) A(z):~ if char(k) = 2 ~(z)n%11(1 - zn)-gn }~[f(z)K(1+z2n-1)g2n-I/(1-z2n) g2n n=1 where f(z) = (I - T(z) - z-IT(z)2)-1(1 if char(k) # 2 - z - T(z)) -I is rational- oa (b ) B ( ~ ) = ( I -- Z 2 )- I ( i I z )- I G ( z )2 ~ ( ] + zns(z) ) n= I (e) C(z) = (t - z2)-1(1 - z)-lG(z)2"~(1 n=l - znG(z)) -I (d) D(z) = (O'G)(z2)G(z)fi(1 n=O + gn zn+1) (e) E(z) = ( G ' G ) ( z 2 ) G ( z ) ~ ( I n=O - gnzn+]) -I \ ay Proof N'See [An-l, prop.

D n A map u/~ ~(k) , ]til = d i . ,tn > F . p. algebra over F ; FE~}. p. p. algebra over surjective. F set is countable: = {finite presentations derived from the finite presentation. ,tn> is countable there are countably many finite presentations ~/~ is countable, of this standard form in standard form of the prime fields} is countable. elements of the graded algebra the following countably be any countable field, then a simple extension there are only countably many simple extensions = {finite extensions (k) F A = B 8ko k to a field A k .

Akad. G. Bon~ev" BI. 8 1113 Sofia, Bulgaria S, Halperin Department of Mathematics University of Toronto Toronto Canada M5S IAI HILBERT SERIES OF FINITELY PRESENTED ALGEBRAS by David A-NICK and Clas LOFWALL Summary Let / denote the collection of all Hilbert connected graded algebras over a field This paper addresses series of finitely presented k . What can we say about the s e t / ? itself to that question. In 1974 Govorov conjectured that only rational power series b e l o n g e d t o ~ . was first disproved by Shearer [Go-2] This conjecture [Sh] , using methods which we will generalize and extend in this paper.

### Algebra, Algebraic Topology and their Interactions: Proceedings of a Conference held in Stockholm, Aug. 3 - 13, 1983, and later developments by Jan-Erik Roos

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