A Cancellation Theorem for Projective Modules over Finitely Generated Rings

1988 ◽  
pp. 281-287 ◽  
Author(s):  
N. MOHAN KUMAR ◽  
M. Pavaman MURTHY ◽  
A. ROY
Keyword(s):  
Projective Modules ◽  
Finitely Generated ◽  
Cancellation Theorem

scholarly journals On finitely generated n-SG-projective modules

2010 ◽  
Vol 121 (1) ◽  
pp. 35-44
Author(s):  
Driss Bennis
Keyword(s):  
Projective Modules ◽  
Finitely Generated

3.—A Note on Projective Modules

1976 ◽  
Vol 75 (1) ◽  
pp. 24-31 ◽  
Author(s):  
P. F. Smith
Keyword(s):  
Noetherian Rings ◽  
Projective Modules ◽  
Finitely Generated ◽  
Right Noetherian Rings

SynopsisFor various classes of right noetherian rings it is shown that projective right modules are either finitely generated or free.

scholarly journals Recollement of homotopy categories and Cohen-Macaulay modules

2011 ◽  
Vol 8 (3) ◽  
pp. 507-542 ◽  
Author(s):  
Osamu Iyama ◽  
Kiriko Kato ◽  
Jun-ichi Miyachi
Keyword(s):  
Homotopy Category ◽  
Module Category ◽  
Gorenstein Ring ◽  
Projective Modules ◽  
Finitely Generated ◽  
Stable Module Category ◽  
Quotient Category ◽  
Stable Module

AbstractWe study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. In the case of the homotopy category of finitely generated projective modules over an Iwanaga-Gorenstein ring, we show the existence of a new structure in the above quotient category, which we call a triangle of recollements. Moreover, we show that this quotient category is triangle equivalent to the stable module category of Cohen-Macaulay T2(R)-modules.

scholarly journals FINITE DOMINATION AND NOVIKOV RINGS. ITERATIVE APPROACH

2012 ◽  
Vol 55 (1) ◽  
pp. 145-160 ◽  
Author(s):  
THOMAS HÜTTEMANN ◽  
DAVID QUINN
Keyword(s):  
Laurent Series ◽  
Chain Complex ◽  
Laurent Polynomial ◽  
Projective Modules ◽  
Finitely Generated ◽  
Formal Laurent Series ◽  
Chain Complexes ◽  
Laurent Polynomial Ring ◽  
Bounded Below ◽  
Free Modules

AbstractSuppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x−1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ⊗LR((x)) and C ⊗LR((x−1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology34(3) (1995), 619–632). Here R((x)) = R[[x]][x−1] and R((x−1)) = R[[x−1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

scholarly journals Isomorphisms between endomorphism rings of projective modules

1993 ◽  
Vol 35 (3) ◽  
pp. 353-355 ◽  
Author(s):  
José Luis García ◽  
Juan Jacobo Simón
Keyword(s):  
Morita Equivalence ◽  
Projective Modules ◽  
Finitely Generated ◽  
Endomorphism Rings ◽  
Morita Equivalent ◽  
Free Modules

Let R and S be arbitrary rings, RM and SN countably generated free modules, and let φ:End(RM)→End(sN) be an isomorphism between the endomorphism rings of M and N. Camillo [3] showed in 1984 that these assumptions imply that R and S are Morita equivalent rings. Indeed, as Bolla pointed out in [2], in this case the isomorphism φ must be induced by some Morita equivalence between R and S. The same holds true if one assumes that RM and SN are, more generally, non-finitely generated free modules.

scholarly journals Flat modules and lifting of finitely generated projective modules

2005 ◽  
Vol 220 (1) ◽  
pp. 49-68 ◽  
Author(s):  
Alberto Facchini ◽  
Dolors Herbera ◽  
Iskhak Sakhajev
Keyword(s):  
Projective Modules ◽  
Finitely Generated ◽  
Flat Modules

scholarly journals A note on deformations of Gorenstein-projective modules over finite dimensional algebras

2019 ◽  
Vol 53 (supl) ◽  
pp. 245-256 ◽  
Author(s):  
José A. Vélez-Marulanda
Keyword(s):  
Projective Modules ◽  
Finitely Generated ◽  
Universal Deformation Rings ◽  
Finite Dimensional ◽  
Gorenstein Projective Modules ◽  
Deformation Rings ◽  
Finite Dimensional Algebras

In this note, we present a survey of results concerning universal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional algebras.

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