By Jörgen Backelin, Jürgen Herzog, Herbert Sanders (auth.), Luchezar L. Avramov, Kerope B. Tchakerian (eds.)
ISBN-10: 3540459944
ISBN-13: 9783540459941
ISBN-10: 3540503714
ISBN-13: 9783540503712
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Extra resources for Algebra Some Current Trends: Proceedings of the 5th National School in Algebra held in Varna, Bulgaria, Sept. 24 – Oct. 4, 1986
Sample text
London Math. Soc. (2) 13 (1976), 438--442. [M] J. MILNOR, Introduction to algebraic K-theory, (Annals of Math. Studies No. 72, Princeton, 1971). [R] N. ROBY, A/g~bres de Clifford des formes polynomes, C. R. Acad. Sc. Paris 268 (1969), 484-486. [Sch] W. SCHARLAU,Quadratic and Hermitian Forms, Grundlehren 270, Springer-Verlag, Berlin Heidelberg, 1985. [St] U. STORCH, Die Picard-Zahlen der Singularit~ten t~~ + t~22+ t"2 + t~" = 0, J. Reine Angew. Math. 850 (1984), 188-202. [u] B. ULRICH, Gorenstein rings and modules with high numbers of generators, Math.
English translation: Math. , 11 (1977), 221-238). 8. Z. V. Mikhalev. Elementary subgroup of a unitary group over a PI-ring (in Russian). Vest. Mosk. , Ser. I, No. I (]985), 30-36. (English translation: Mosc. Univ. Math. Bull. 40, No. 1, 44-54 (1985)). 9. I. Zel'manov. Isomorphisms of linear groups over associative rings (in Russian). Sib. Mat. , 26 (1985)~ No. 4, 49-67. (English translation: ~ib. Math. , 26 (1986), 515-830). I0. Z. Anan'in. Presentable varieties of algebras (in Russian). Novosibirsk, 1986, 21 pp.
El-1 is a regular sequence, it follows t h a t R / ( x l , ~ o ' . . " ~ - 1 ) ~-- C [ X 1 , X 2 , X s ] / ( X I , a o ' . . " a~-l) is C M of d i m R - 1. Hence ( x l , a 0 • . . • 0~-1) is a non-principal CM-ideal, which implies that [ ( ~ , a 0 . . - < - 1 ) ] ¢ 0. [] REMARK. For d = 2 the divisor class group C£(R) of R -. C[X1,X2, X 3 ] / ( X d + X d + X d) equals Z[M] and is isomorphic to Z / 2 Z . However, for d > 2, Z - [M] only generates t h e discrete part of ~ ( R ) , as we were told by Storch (see [St]).
Algebra Some Current Trends: Proceedings of the 5th National School in Algebra held in Varna, Bulgaria, Sept. 24 – Oct. 4, 1986 by Jörgen Backelin, Jürgen Herzog, Herbert Sanders (auth.), Luchezar L. Avramov, Kerope B. Tchakerian (eds.)
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