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- W4220809598 abstract "For a commutative ring A we consider a related graph, Γ(A), whose vertices are the unimodular rows of length 2 up to multiplication by units. We prove that Γ(A) is path-connected if and only if A is a GE2-ring, in the terminology of P. M. Cohn. Furthermore, if Y(A) denotes the clique complex of Γ(A), we prove that Y(A) is simply connected if and only if A is universal for GE2. More precisely, our main theorem is that for any commutative ring A the fundamental group of Y(A) is isomorphic to the group K2(2,A) modulo the subgroup generated by symbols." @default.
- W4220809598 created "2022-04-03" @default.
- W4220809598 creator A5038257292 @default.
- W4220809598 date "2022-10-01" @default.
- W4220809598 modified "2023-09-25" @default.
- W4220809598 title "GE2-rings and a graph of unimodular rows" @default.
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- W4220809598 doi "https://doi.org/10.1016/j.jpaa.2022.107074" @default.
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