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The Natural Middle of a Complete Resolution.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The Natural Middle of a Complete Resolution./
作者:	Aduddell, Rebekah J.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	191 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28826491
ISBN:	9798544286424

The Natural Middle of a Complete Resolution.
Aduddell, Rebekah J.

The Natural Middle of a Complete Resolution. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 191 p.

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--The University of Texas at Arlington, 2021.

This item must not be sold to any third party vendors.

It is widely known that minimal free resolutions of a module over a complete intersection ring have nice patterns that arise in their Betti sequences. In the late 1990's Avramov, Gasharov and Peeva defined a new class of R-modules that would exhibit similar patterns in their free resolutions. In doing so, they additionally defined the notion of critical degree for an R-module, which serves as a "flag" for when such patterns arise in the module's Betti sequence. The main purpose of this thesis is to present an extension of critical degree to the category of totally acyclic complexes, Ktac(R), where R is a commutative Noetherian, local ring. Furthermore, we will provide an appropriate dual analogue and then look towards realizing the cohomological characterization for these notions, utilizing the original such characterization. With regard to this topic, our attention will predominantly turn towards when R is further assumed to be a complete intersection ring of the form R = Q/(f1,..., fc) where (Q, m, k) is a regular local ring and f1,..., fc a Q-regular sequence in the maximal ideal, m.We then investigate how the critical and cocritical degrees of an R-complex may change under certain operations of R-complexes, such as translations, direct sums, and tensoring with a bounded complex. Lastly, we introduce a new invariant of R-complexes and R-modules called the critical width, or diameter, which we define to be the "distance" between the critical and cocritical degrees of an R-complex.

ISBN: 9798544286424Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Complete resolutions

The Natural Middle of a Complete Resolution.
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245 1 4 $a The Natural Middle of a Complete Resolution.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 191 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
500 $a Advisor: Jorgensen, David.
502 $a Thesis (Ph.D.)--The University of Texas at Arlington, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a It is widely known that minimal free resolutions of a module over a complete intersection ring have nice patterns that arise in their Betti sequences. In the late 1990's Avramov, Gasharov and Peeva defined a new class of R-modules that would exhibit similar patterns in their free resolutions. In doing so, they additionally defined the notion of critical degree for an R-module, which serves as a "flag" for when such patterns arise in the module's Betti sequence. The main purpose of this thesis is to present an extension of critical degree to the category of totally acyclic complexes, Ktac(R), where R is a commutative Noetherian, local ring. Furthermore, we will provide an appropriate dual analogue and then look towards realizing the cohomological characterization for these notions, utilizing the original such characterization. With regard to this topic, our attention will predominantly turn towards when R is further assumed to be a complete intersection ring of the form R = Q/(f1,..., fc) where (Q, m, k) is a regular local ring and f1,..., fc a Q-regular sequence in the maximal ideal, m.We then investigate how the critical and cocritical degrees of an R-complex may change under certain operations of R-complexes, such as translations, direct sums, and tensoring with a bounded complex. Lastly, we introduce a new invariant of R-complexes and R-modules called the critical width, or diameter, which we define to be the "distance" between the critical and cocritical degrees of an R-complex.
590 $a School code: 2502.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Complete resolutions
653 $a Critical degrees
653 $a Totally acyclic complexes
653 $a Complete intersection rings
653 $a Operations of complexes
653 $a Codepth
653 $a Cosocle
690 $a 0405
690 $a 0642
710 2 $a The University of Texas at Arlington. $b Mathematics. $3 1682219
773 0 $t Dissertations Abstracts International $g 83-05B.
790 $a 2502
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28826491