  In this paper, we define and study absolute matrix order ideals in absolute
matrix order unit spaces. As an application of absolute matrix order unit
property, we construct some kinds of absolute matrix order ideals in absolute
matrix order unit spaces. Later, we show that the Grothendieck group of a such
kind of absolute matrix order ideal for order projections is a subgroup of
Grothendieck group of corresponding absolute matrix order unit space for order
projections.
