Lectures On Modules And Rings

By Katharina Weiss. 2016

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𝔏-Rickart Modules (2015, background): “51 in [16] to an analogous module case.”
Graded Rings and Graded Grothendieck Groups (2014, methodology): “For the theory of (non-graded) Morita theory we refer the reader to [62] and [4]”
Trace Ideals and Centers of Endomorphism Rings of Modules over Commutative Rings (2016, background): “For example, a finitely generated ideal is the trace ideal of a projective module if and only if it is idempotent, and τM (R) = R if and only if every finitely generated R-module is a homomorphic image of a direct sum of copies of M ; see [9], [19] and Section 2.”
Singular Intersection Homology (2020, background): “Our favored sources include topology texts by Hatcher [124], Munkres [178, 177], Dold [71], Spanier [214], Bredon [38], and Davis and Kirk [67]; books on PL topology by Hudson [128] and Rourke and Sanderson [192]; algebra books by Lang [145], Lam [144], and Bourbaki [30]; homological algebra books b”
Tensor categorical foundations of algebraic geometry (2014, background): “If X is a scheme (or more generally an algebraic stack), which has the strong resolution property, then locally free OX-modules constitute a dense subcategory of Qcoh(X): For every M ∈ Qcoh(X) we have M ∼= colimV→M,V locally free V. Recall that the Theorem of Lazard-Govorov ([Lam99, Theorem 4.34]) s”
Derived Categories (2016, methodology): “Sources for this material are [Rot] and [Lam].”