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The crossed product theorem for projective Schur algebras

Published online by Cambridge University Press:  04 June 2001

E. Choi  and
H. Lee
E. Choi
Affiliation:
Department of Mathematics, Hannam University, Taejon, Korea e-mail:emc@math.hannam.ac.kr
H. Lee
Affiliation:
Department of Mathematics, Ewha Womans University, Seoul, Korea e-mail:hsllee@mm.ewha.ac.kr
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The projective Schur group of a commutative ring was introduced by Lorenz and Opolka. It was revived by Nelis and Van Oystaeyen, and later by Aljadeff and Sonn. In this paper we study the intriguing question that there seems to be no adequate version of the crossed product theorem for the projective Schur group. We present a radical group R(k) (k a field) situated between the Schur group and the projective Schur group, and we prove the crossed product theorem for R(k).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 1 , January 2001 , pp. 135 - 143
Copyright
2001 Glasgow Mathematical Journal Trust