Download e-book for kindle: Ring Theory: Proceedings of an International Conference held by J. Alev (auth.), Freddy M. J. van Oystaeyen (eds.)

By J. Alev (auth.), Freddy M. J. van Oystaeyen (eds.)

ISBN-10: 3540164960

ISBN-13: 9783540164968

ISBN-10: 3540398333

ISBN-13: 9783540398332

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Extra resources for Ring Theory: Proceedings of an International Conference held in Antwerp, April 1–5, 1985

Example text

To prove iv, let ~ X , X -l] , I[Y, y-l] and FIT, T -I] be the graded residue class fields of R Psgh , R qsgh , and B s. We allready know that k, i and F are separably closed. As R is quasistrongly graded, des X = des Y = I, so des T = I and B s is strictly gr-henselian. (Bs is one of the components of the considered tensor product). 11. Example. The conclusion of iv) does not hold for arbitrary rings, as the following example shows. Let R be the ring of algebraic integers in a o number field and Pl a prime number, such that the ideal PiRo is a product of two prime ideals P and Q.

Hence R is gr-local. 2). Suppose that R' is a gr-~tale R-algebra, n a graded prime of R' and R'/n ~ R/m, then R ÷ Qg(R') is a gr-~tale covering, Finally, so it has a section. 6 below, it then follows that R mg Q~(R). suppose that k = R/m is not gr-separably closed. Let L be a gr-separable extension of K, then L = ~ ~ . Lift the (homogeneous) minimal polynomial f to a monic homogeneous polynomial f and let R' = ~ ~ /(f), then clearly R' is gr-~tale over R, so R + R' splits, hence f has a root within R, and f has a root within k.

London Math. Soc. (3) 29 (1974) 237-256. 14. F. W. Long, The Brauer group of dimodule algebras, J. Algebra, 559-601. 15. F. W. Long, Generalized Clifford algebras and dimodule algebras, J. London Math. Soc. (2) 13 (1976), 438-442. 16. A. O. Morris, On a generalized Clifford algebra, Quart. J. of Math. (2) 18 (1967), 7-12. 17. A. O. Morris, On a generalized Clifford algebra (If), Quart. J. of Math. (Oxford) (2) 19 (1968), 289-299. 18. M. Orzech, On the Brauer group of modules having a grading and an action, Canad.

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Ring Theory: Proceedings of an International Conference held in Antwerp, April 1–5, 1985 by J. Alev (auth.), Freddy M. J. van Oystaeyen (eds.)


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