Integral closure of ideals, rings, and modules

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Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs (2010, background): “We refer to [15] for general background on the reduction and the integral closure of ideals.”
Hilbert Functions of Filtered Modules (2007, background): “maximal M-superficial sequence is a minimal M-reduction of q (see [54] and [10]).”
Powers of sums and their homological invariants (2016, background): “n−1x+ an = 0 where n≥ 1,ai ∈ Ii for 1 ≤ i≤ n. The integral closure is an ideal containing I, and if Iis a monomial ideal then so is I: In fact, by Proposition 1.4.2 and the discussion preceding it in [36], Iis generated by monomials f∈ Rsuch that fr∈ Ir for some r≥ 1. For each s≥ 1, let I(s) = T P∈M”
The index of an algebraic variety (2012, background): “with for instance, [53], B.”