Elements of Small Orders in K 2 F II

Jerzy Browkin

doi:10.1007/s11401-006-0543-3

Chinese Annals of Mathematics, Series B ›› 2007, Vol. 28 ›› Issue (5) : 507 -520. DOI: 10.1007/s11401-006-0543-3

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Elements of Small Orders in K ₂ F II

Jerzy Browkin ¹^,^a

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Abstract

In "Elements of small orders in K ₂(F)" (Algebraic K-Theory, Lecture Notesin Math., 966, 1982, 1–6.), the author investigates elements of the form {a, Φn(a)} in theMilnor group K ₂ F of a field F, where Φn(x) is the n-th cyclotomic polynomial. In thispaper, these elements are generalized. Applying the explicit formulas of Rosset and Tatefor the transfer homomorphism for K ₂, the author proves some new results on elements ofsmall orders in K ₂ F.

Keywords

Cyclotomic elements in K ₂ F / Transfer in K-theory / Milnor group / 11R70 / 19F15

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Jerzy Browkin. Elements of Small Orders in K ₂ F II. Chinese Annals of Mathematics, Series B, 2007, 28(5): 507-520 DOI:10.1007/s11401-006-0543-3

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References

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[1]	Browkin Lecture Notes in Math., 1982, 966: 1

[2]	Urbanowicz J. Pure Appl. Algebra, 1988, 50: 295

[3]	Rosset Comment. Math. Helvetici, 1983, 58: 38

[4]	Milnor, J., Introduction to Algebraic K-Theory, Ann. of Math. Studies, 72, Princeton Univ. Press, Princeton, 1971.

[5]	Bass Lecture Notes in Math, 1971, 244: 233

[6]	Suslin, A. A., Torsion in K ₂ of fields, K-Theory, 1, 1987, 5–29.

[7]	Delone, B. N. and Faddeev, D. K., The theory of irrationalities of the third degree (in Russian), TrudyMat. Inst. Steklov, 11, 1940, 1–340; English translation, Providence, 1964.