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 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.
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.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  1999 May 22 
Publisher  
ISBN (Print)  9162835785 
Publication status  Published  1999 
Bibliographical note
Defence detailsDate: 19990522
Time: 10:00
Place: Mathematics Building, Sölvegatan 18, Room MH:C
External reviewer(s)
Name: Fröberg, Ralf
Title: [unknown]
Affiliation: Stockholm University

Subject classification (UKÄ)
 Mathematics
Free 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