We prove that two, apparently different, class-group valued Galois module structure invariants associated to the algebraic $K$-groups of rings of algebraic integers coincide. This comparison result is particularly important in making explicit calculations.

MSC Classifications:

11S99, 19F15, 19F27 show english descriptions None of the above, but in this section
Symbols and arithmetic [See also 11R37]
Etale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10] 11S99 - None of the above, but in this section
19F15 - Symbols and arithmetic [See also 11R37]
19F27 - Etale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]

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