A NOTE ON K-THEORY OF AZUMAYA ALGEBRAS

被引：4

作者：

Hazrat, Roozbeh ^{[1
]}

Millar, Judith R. ^{[1
]}

机构：

[1] Queens Univ Belfast, Dept Pure Math, Belfast BT7 1NN, Antrim, North Ireland

来源：

COMMUNICATIONS IN ALGEBRA | 2010年 / 38卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Azumaya algebras; K-Theory; DIVISION-ALGEBRAS;

D O I：

10.1080/00927870902828710

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an Azumaya algebra A which is free over its centre R, we prove that K-theory of A is isomorphic to K-theory of R up to its rank torsions. We conclude that K-i(A, Z/m) = K-i(R, Z/m) for any m relatively prime to the rank and i >= 0. This covers, for example, K-theory of division algebras, K-theory of Azumaya algebras over semilocal rings, and K-theory of graded central simple algebras indexed by a totally ordered abelian group.

引用

页码：919 / 926

页数：8

共 19 条

[1]

[Anonymous], 1989, ALGEBRA

[2]

[Anonymous], 1991, Quadratic and Hermitian Forms over Rings

[3]

Auslander M., 1960, T AM MATH SOC, V97, P367, DOI DOI 10.2307/1993378

[4]

AZUMAYA G., 1951, Nagoya Math. J., V2, P119

[5]

BASS H, 1967, TATA I FUNDAMENTAL R, V0041

[6] THE GRADED ORDER OF A VALUED DIVISION ALGEBRA [J].

BOULAGOUAZ, M .

COMMUNICATIONS IN ALGEBRA, 1995, 23 (11) :4275-4300

[7]

Bourbaki Nicolas, 1989, Elements of Mathematics (Berlin)

[8] HOMOLOGY OF AZUMAYA ALGEBRAS [J].

CORTINAS, G ;

WEIBEL, C .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 121 (01) :53-55

[9]

DAWKINS BP, 1966, CAN J MATH, V18, P1333

[10]

Green S., 1978, J PURE APPL ALGEBRA, V12, P153

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