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The Golod Property on Monomial Rings
Başlık:
The Golod Property on Monomial Rings
Yazar:
Gilbert, Cody M., author.
ISBN:
9780355987072
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (89 pages)
Genel Not:
Source: Masters Abstracts International, Volume: 57-06M(E).
Advisors: William F. Moore Committee members: Hugh N. Howards; Ellen E. Kirkman.
Özet:
In this paper, we work towards understanding a counterexample found in Lukas Katthan's "A non-Golod Ring with a Trivial Product on its Koszul Homology". In this counterexample, Katthan disproved a claim made by Berglund and Jollenbeck which stated that a monomial ring is Golod if and only if the product on its Koszul Homology is trivial. At the end, we find a non-Golod monomial ring with trivial product on its Koszul homology, so we will need the backwards direction to be stronger in order for this statement to be true.
In order to understand what a Golod ring is, we first learn about complexes, differential graded algebras, spectral sequences and Massey products. After this, we spend some effort learning about the Taylor complex and its relation to the Koszul complex, as we will actually be looking at products in the homology of the Taylor complex tensored with a field k, which is isomorphic to the homology of the Koszul complex, in order to make computations easier.
Notlar:
School code: 0248
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(692296.1) | 692296-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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