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Seminar

Fellowship of the Ring: Cancellation of Finite-Dimensional Noetherian Modules November 30, 2021 (01:00 PM PST - 02:30 PM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Robin Baidya (University of Tennessee)
Description No Description
Video

Fellowship Of The Ring: Cancellation Of Finite-Dimensional Noetherian Modules

Abstract/Media

To attend this seminar, you must register in advance, by clicking HERE.

The Module Cancellation Problem solicits hypotheses that, when imposed on modules K, L, and M over a ring S, afford the implication K⊕L≅K⊕M⟹L≅M.  In a well-known paper on basic element theory from 1973, Eisenbud and Evans lament the "great scarcity of strong results" in module cancellation research, expressing the wish that, "under some general hypothesis" on finitely generated modules over a commutative Noetherian ring, cancellation could be demonstrated.  Singling out cancellation theorems by Bass and Dress that feature "large" projective modules, Eisenbud and Evans contend further that, although "[s]ome criteria of 'largeness' is certainly necessary in general [. . . ,] the need for projectivity is not clear."  In this talk, we will contextualize the preceding entreaty of Eisenbud and Evans, offer a response to it, and then construct a cancellation example that simultaneously eludes many observations from the module cancellation literature.  Along the way, we will discuss some unanswered questions in the hopes of giving direction to this broad area of research.

92080?type=thumb Cancellation of Finite-Dimensional Noetherian Modules 264 KB application/pdf

Fellowship Of The Ring: Cancellation Of Finite-Dimensional Noetherian Modules