On λ-pure acyclic complexes in a Grothendieck category

2019 ◽  
Vol 525 ◽  
pp. 245-258
Author(s):  
Esmaeil Hosseini
Keyword(s):  
Grothendieck Category ◽  
Acyclic Complexes

Azaoxa Macrocyclic and Acyclic Complexesof Lanthanides

1998 ◽  
Vol 63 (3) ◽  
pp. 363-370 ◽  
Author(s):  
Violetta Patroniak-Krzyminiewska ◽  
Wanda Radecka-Paryzek
Keyword(s):  
Schiff Base ◽  
Spectral Data ◽  
Macrocyclic Ligand ◽  
Lanthanide Ions ◽  
H Nmr ◽  
Elemental Analyses ◽  
Acyclic Complexes ◽  
Schiff Base Cyclocondensation

The template reactions of 2,6-diacetylpyridine with 3,6-dioxaoctane-1,8-diamine in the presence of dysprosium(III), thulium(III) and lutetium(III) chlorides and erbium(III) perchlorate produce the complexes of 15-membered macrocyclic ligand with an N3O2 set of donor atoms as a result of the [1+1] Schiff base cyclocondensation. In contrast, analogous reactions involving the lighter lanthanide ions (lanthanum(III), samarium(III) and europium(III)) yield the acyclic complexes with terminal acetylpyridyl groupings as products of the partial [2+1] condensation. The complexes were characterized by spectral data (IR, UV-VIS, 1H NMR, MS), and thermogravimetric and elemental analyses.

scholarly journals Gorenstein Projective Modules over Triangular Matrix Rings

2016 ◽  
Vol 23 (01) ◽  
pp. 97-104 ◽  
Author(s):  
H. Eshraghi ◽  
R. Hafezi ◽  
Sh. Salarian ◽  
Z. W. Li
Keyword(s):  
Triangular Matrix ◽  
Projective Modules ◽  
Matrix Rings ◽  
Matrix Algebras ◽  
Gorenstein Projective Modules ◽  
Artin Algebras ◽  
Acyclic Complexes ◽  
Matrix Extension

Let R and S be Artin algebras and Γ be their triangular matrix extension via a bimodule SMR. We study totally acyclic complexes of projective Γ-modules and obtain a complete description of Gorenstein projective Γ-modules. We then construct some examples of Cohen-Macaulay finite and virtually Gorenstein triangular matrix algebras.

scholarly journals Matrix factorizations for self-orthogonal categories of modules

2020 ◽  
pp. 2150037
Author(s):  
Petter Andreas Bergh ◽  
Peder Thompson
Keyword(s):  
Commutative Ring ◽  
Regular Element ◽  
Homotopy Category ◽  
Matrix Factorizations ◽  
Natural Embedding ◽  
Acyclic Complexes

For a commutative ring [Formula: see text] and self-orthogonal subcategory [Formula: see text] of [Formula: see text], we consider matrix factorizations whose modules belong to [Formula: see text]. Let [Formula: see text] be a regular element. If [Formula: see text] is [Formula: see text]-regular for every [Formula: see text], we show there is a natural embedding of the homotopy category of [Formula: see text]-factorizations of [Formula: see text] into a corresponding homotopy category of totally acyclic complexes. Moreover, we prove this is an equivalence if [Formula: see text] is the category of projective or flat-cotorsion [Formula: see text]-modules. Dually, using divisibility in place of regularity, we observe there is a parallel equivalence when [Formula: see text] is the category of injective [Formula: see text]-modules.

Generalized Grothendieck category

1988 ◽  
Vol 28 (5) ◽  
pp. 734-739
Author(s):  
V. G. Gorbunov
Keyword(s):  
Grothendieck Category

scholarly journals Totally acyclic complexes over noetherian schemes

2011 ◽  
Vol 226 (2) ◽  
pp. 1096-1133 ◽  
Author(s):  
Daniel Murfet ◽  
Shokrollah Salarian
Keyword(s):  
Acyclic Complexes
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