K1 of twisted rings of polynomials

Bernard Badzioch

doi:10.1023/A:1007700812931

K₁ of twisted rings of polynomials

Bernard Badzioch

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove that for an arbitrary endomorphism α of a ring R the group K₁(R_α[t]) splits into the direct sum of K₁(R) and Nil(R; α). Moreover, for any such R and α Nil(R; α) is isomorphic to Nil(R′; α′) for some ring R′ with a′: R′ → R′ - an isomorphism.

Original language	English
Pages (from-to)	29-34
Number of pages	6
Journal	K-Theory
Volume	16
Issue number	1
DOIs	https://doi.org/10.1023/A:1007700812931
State	Published - 1999

Keywords

Lower algebraic k-theory
Nil
Twisted ring of polynomials

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10.1023/A:1007700812931

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abstract = "We prove that for an arbitrary endomorphism α of a ring R the group K1(Rα[t]) splits into the direct sum of K1(R) and Nil(R; α). Moreover, for any such R and α Nil(R; α) is isomorphic to Nil(R′; α′) for some ring R′ with a′: R′ → R′ - an isomorphism.",

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T1 - K1 of twisted rings of polynomials

AU - Badzioch, Bernard

PY - 1999

Y1 - 1999

N2 - We prove that for an arbitrary endomorphism α of a ring R the group K1(Rα[t]) splits into the direct sum of K1(R) and Nil(R; α). Moreover, for any such R and α Nil(R; α) is isomorphic to Nil(R′; α′) for some ring R′ with a′: R′ → R′ - an isomorphism.

AB - We prove that for an arbitrary endomorphism α of a ring R the group K1(Rα[t]) splits into the direct sum of K1(R) and Nil(R; α). Moreover, for any such R and α Nil(R; α) is isomorphic to Nil(R′; α′) for some ring R′ with a′: R′ → R′ - an isomorphism.

KW - Lower algebraic k-theory

KW - Nil

KW - Twisted ring of polynomials

UR - https://www.scopus.com/pages/publications/0041172560

U2 - 10.1023/A:1007700812931

DO - 10.1023/A:1007700812931

M3 - Article

AN - SCOPUS:0041172560

SN - 0920-3036

VL - 16

SP - 29

EP - 34

JO - K-Theory

JF - K-Theory

IS - 1

ER -

K₁ of twisted rings of polynomials

Abstract

Keywords

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