Complexes and Diffrerential Graded Modules
(1999) In Doctoral Theses in Mathematical Sciences 1999:3. Abstract
 The main topic of the thesis is the generalization of some traditional moduletheoretic homological applications to complexes of modules and to differential graded modules over differential graded rings.
We introduce three possible generalizations of the classical notion of annihilator of an <i>R</i>module. For linear functors D (<i>R</i>) > D (<i>R</i>), preserving the triangulation, certain inclusion results for these annihilators are obtained.
We study ascent and descent of Gorenstein and CohenMacaulay properties along a local homomorphism <i>f</i>:<i>R > S</i> in the presence of a finite <i>S</i>module which is of... (More)  The main topic of the thesis is the generalization of some traditional moduletheoretic homological applications to complexes of modules and to differential graded modules over differential graded rings.
We introduce three possible generalizations of the classical notion of annihilator of an <i>R</i>module. For linear functors D (<i>R</i>) > D (<i>R</i>), preserving the triangulation, certain inclusion results for these annihilators are obtained.
We study ascent and descent of Gorenstein and CohenMacaulay properties along a local homomorphism <i>f</i>:<i>R > S</i> in the presence of a finite <i>S</i>module which is of finite flat dimension over <i>R</i> thus generalizing the concept of <i>homomorhism of finite flat dimension</i> introduced by Luchezar Avramov and HansBjørn Foxby.
The two approaches of the classical homological algebra to homological dimensions (the resolutional approach and the functorial one) give rise to different invariants in the category of differential graded modules over a differential graded ring. We study this dichotomy and establish the simultaneous finiteness of the resolutional and the functorial flat dimension in one special case.
We also generalize the notion of <i>the canonical module of a CohenMacaulay ring</i> to the case of a genuine differential graded ring. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/39582
 author
 Apassov, Dmitri ^{LU}
 supervisor
 opponent

 Fröberg, Ralf, Stockholm University
 organization
 publishing date
 1999
 type
 Thesis
 publication status
 published
 subject
 keywords
 algebraic geometry, field theory, Number Theory, fiber of a local homomorphism, DG dualizing module, homological dimensions, differential graded rings, almost finite module, CohenMacaulay rings, local homomorphism, Gorenstein rings, annihilator, complex of modules, algebra, group theory, Talteori, fältteori, algebraisk geometri, gruppteori
 in
 Doctoral Theses in Mathematical Sciences
 volume
 1999:3
 pages
 55 pages
 publisher
 Centre for Mathematical Sciences, Lund University
 defense location
 Mathematics Building, Sölvegatan 18, Room MH:C
 defense date
 19990522 10:00:00
 external identifiers

 other:ISRN: LUNFMA10111999
 ISSN
 14040034
 ISBN
 9162835785
 language
 English
 LU publication?
 yes
 id
 c8b1cb4f4fa44a34aa932d0f5a2d2e97 (old id 39582)
 date added to LUP
 20160401 16:14:55
 date last changed
 20190521 13:25:18
@phdthesis{c8b1cb4f4fa44a34aa932d0f5a2d2e97, abstract = {{The main topic of the thesis is the generalization of some traditional moduletheoretic homological applications to complexes of modules and to differential graded modules over differential graded rings.<br/><br> <br/><br> We introduce three possible generalizations of the classical notion of annihilator of an <i>R</i>module. For linear functors D (<i>R</i>) > D (<i>R</i>), preserving the triangulation, certain inclusion results for these annihilators are obtained.<br/><br> <br/><br> We study ascent and descent of Gorenstein and CohenMacaulay properties along a local homomorphism <i>f</i>:<i>R > S</i> in the presence of a finite <i>S</i>module which is of finite flat dimension over <i>R</i> thus generalizing the concept of <i>homomorhism of finite flat dimension</i> introduced by Luchezar Avramov and HansBjørn Foxby.<br/><br> <br/><br> The two approaches of the classical homological algebra to homological dimensions (the resolutional approach and the functorial one) give rise to different invariants in the category of differential graded modules over a differential graded ring. We study this dichotomy and establish the simultaneous finiteness of the resolutional and the functorial flat dimension in one special case.<br/><br> <br/><br> We also generalize the notion of <i>the canonical module of a CohenMacaulay ring</i> to the case of a genuine differential graded ring.}}, author = {{Apassov, Dmitri}}, isbn = {{9162835785}}, issn = {{14040034}}, keywords = {{algebraic geometry; field theory; Number Theory; fiber of a local homomorphism; DG dualizing module; homological dimensions; differential graded rings; almost finite module; CohenMacaulay rings; local homomorphism; Gorenstein rings; annihilator; complex of modules; algebra; group theory; Talteori; fältteori; algebraisk geometri; gruppteori}}, language = {{eng}}, publisher = {{Centre for Mathematical Sciences, Lund University}}, school = {{Lund University}}, series = {{Doctoral Theses in Mathematical Sciences}}, title = {{Complexes and Diffrerential Graded Modules}}, volume = {{1999:3}}, year = {{1999}}, }