Nontriviality of SK1 (R [MJ)
نویسنده
چکیده
The main result of this paper is as follows: For any commutative regular (actually even K2-regular) ring R and any finitely generated intermediate monoid ZP+ c A4 c Q’+ (for some natural r) the following conditions are equivalent: (a) A4 zE:, (b) R[M] is K,-regular, (c) M is seminormal and SK,(R) = SK,(R[M]) (i.e. the natural homomorphism SK,(R) -SK,(R[M]) is an isomorphism), and, if in addition QR # 0, (d) SKI(R) = SK,WCMl), where QR is a module of absolute differentials. The implications (a) j(b) q(c) are well known. In Sections 8-10 we present examples, further generalizations and applications. 1991 Math. Subj. Class.: 19B99, 19C20, 20M25
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تاریخ انتشار 2003