The author extends his results concerning the detecting of algebraic K- theory by ”Bott periodic” algebraic K-theory, introduced in [Algebraic K- theory and cobordism, Mem. Am. Math. Soc. 221 (1979; Zbl 0413.55004)]. For example, if A is a commutative ring with an \(\ell^{\nu}\)-th root of unity, then there results a ”Bott element”, x, in \(K_ 2(A;{\mathbb{Z}}/\ell^{\nu})\). The author characterizes the kernel of the localization map \(\rho: K_ i(A;{\mathbb{Z}}/\ell^{\nu})\to K_ i(A;{\mathbb{Z}}/\ell^{\nu})[1/x],\) in terms of the Hurewicz map \(H: K_ i(A;{\mathbb{Z}}/\ell^{\nu})\to KU_ i(BGLA^+;{\mathbb{Z}}/\ell^{\nu}).\) It is explained how this characterization is related to the Lichtenbaum- Quillen conjecture concerning the algebraic K-theory of schemes. As an application, it is shown that if \(\sigma\in K_{2N}(A;{\mathbb{Z}}/\ell^{\nu})\) has \(H(\sigma)=H(x^ N)\) then there is a diagram of the form.