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Homological algebra for commutative monoids

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TitleInfo
Title
Homological algebra for commutative monoids
Name (type = personal)
NamePart (type = family)
Flores
NamePart (type = given)
Jaret
NamePart (type = date)
1985-
DisplayForm
Jaret Flores
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Weibel
NamePart (type = given)
Charles
DisplayForm
Charles Weibel
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Buch
NamePart (type = given)
Anders
DisplayForm
Anders Buch
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Borisov
NamePart (type = given)
Lev
DisplayForm
Lev Borisov
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Walker
NamePart (type = given)
Mark
DisplayForm
Mark Walker
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact)
2015
DateOther (qualifier = exact); (type = degree)
2015-01
CopyrightDate (encoding = w3cdtf); (qualifier = exact)
2015
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
We first study commutative, pointed monoids providing basic definitions and results in a manner similar commutative ring theory. Included are results on chain conditions, primary decomposition as well as normalization for a special class of monoids which lead to a study monoid schemes, divisors, Picard groups and class groups. It is shown that the normalization of a monoid need not be a monoid, but possibly a monoid scheme. After giving the definition of, and basic results for, A-sets, we classify projective A-sets and show they are completely determine by their rank. Subsequently, for a monoid A, we compute K_0 and K_1 and prove the Devissage Theorem for G_0 . With the definition of short exact sequence for A-sets in hand, we describe the set Ext(X,Y ) of extensions for A-sets X,Y and classify the set of square-zero extensions of a monoid A by an A-set X using the Hochschild cosimplicial set. We also examine the projective model structure on simplicial A-sets showcasing the difficulties involved in computing homotopy groups as well as determining the derived category for a monoid. The author defines the category Da(C) of double-arrow complexes for a class of non-abelian categories C and, in the case of A-sets, shows an adjunction with the category of simplicial A-sets.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_6054
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (vi, 113 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Subject (authority = ETD-LCSH)
Topic
Algebra, Homological
Subject (authority = ETD-LCSH)
Topic
Monoids
Note (type = statement of responsibility)
by Jaret Flores
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3N58P2X
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Flores
GivenName
Jaret
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-12-10 20:10:22
AssociatedEntity
Name
Jaret Flores
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

RULTechMD (ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem (VERSION = 5.1)
windows xp
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