By Jörgen Backelin, Jürgen Herzog, Herbert Sanders (auth.), Luchezar L. Avramov, Kerope B. Tchakerian (eds.)
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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
BEH] R. O. BUCHWEITZ, D. EISENBUD, J. ). [BHU] J. P. BRENNAN, J. HERZOG, B. ULRICH, Maxima/ly generated Cohen-Macaulay modules, to appear in Math. Scand.. [c] L. N. CHILDS, Linearizing of n-lc forms and generalized Clifford a/gebras, Linear and Multilinear Algebra 5 (1978), 267-278. [E] D. EISENBUD, Homologica/ a/gebra on a complete intersection with an application to group representations, Trans. AMS 260 (1980), 35-64. [HI N. HEEREMA, An a/gebra determined by a binary qubic form, Duke math J.
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. Complete text: Depon. 1986, No.
D - 1. But i[P0] = ~ j . : l [ p j ] _- [(Xl, ~, " . . ' < - 1 ) ] . Since f e ( X l , a 0 " . . ' a / - 1 ) , and since X1, a o ' . . " 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 .
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.)