TY - JOUR
T1 - A matrix description for K 1 of graded rings
AU - Zhang, Zuhong
N1 - Publisher Copyright:
© 2016, Hebrew University of Jerusalem.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - The current paper is dedicated to the study of the classical K1 groups of graded rings. Let A be a Γ graded ring with identity 1, where the grading Γ is an abelian group. We associate a category with suspension to the Γ graded ring A. This allows us to construct the group valued functor K1 of graded rings. It will be denoted by K1 gr. It is not only an abelian group but also a ℤ[Γ]-module. From the construction, it follows that there exists “locally” a matrix description of K1 gr of graded rings. The matrix description makes it possible to compute K1 gr of various types of graded rings. The K1 gr satisfies the well known K-theory exact sequence (Formula presented.) for any graded ideal I of A. The above is used to compute K1 gr of cross products.
AB - The current paper is dedicated to the study of the classical K1 groups of graded rings. Let A be a Γ graded ring with identity 1, where the grading Γ is an abelian group. We associate a category with suspension to the Γ graded ring A. This allows us to construct the group valued functor K1 of graded rings. It will be denoted by K1 gr. It is not only an abelian group but also a ℤ[Γ]-module. From the construction, it follows that there exists “locally” a matrix description of K1 gr of graded rings. The matrix description makes it possible to compute K1 gr of various types of graded rings. The K1 gr satisfies the well known K-theory exact sequence (Formula presented.) for any graded ideal I of A. The above is used to compute K1 gr of cross products.
UR - http://www.scopus.com/inward/record.url?scp=84948182768&partnerID=8YFLogxK
U2 - 10.1007/s11856-015-1260-y
DO - 10.1007/s11856-015-1260-y
M3 - Article
AN - SCOPUS:84948182768
SN - 0021-2172
VL - 211
SP - 45
EP - 66
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -