scholarly journals Totally acyclic complexes

2018 ◽  
pp. 137-152
Author(s):  
Alina Iacob
Keyword(s):  
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.

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

scholarly journals Acyclic complexes of finitely generated free modules over local rings

2009 ◽  
Vol 105 (1) ◽  
pp. 85 ◽  
Author(s):  
Meri T. Hughes ◽  
David A. Jorgensen ◽  
Liana M. Sega
Keyword(s):  
Local Ring ◽  
Local Rings ◽  
Finitely Generated ◽  
Reflexive Module ◽  
Commutative Local Ring ◽  
Standard Construction ◽  
Acyclic Complexes ◽  
Free Modules

We consider the question of how minimal acyclic complexes of finitely generated free modules arise over a commutative local ring. A standard construction gives that every totally reflexive module yields such a complex. We show that for certain rings this construction is essentially the only method of obtaining such complexes. We also give examples of rings which admit minimal acyclic complexes of finitely generated free modules which cannot be obtained by means of this construction.

scholarly journals Acyclic Complexes and Gorenstein Rings

2020 ◽  
Vol 27 (03) ◽  
pp. 575-586
Author(s):  
Sergio Estrada ◽  
Alina Iacob ◽  
Holly Zolt
Keyword(s):  
Analogous Result ◽  
Gorenstein Ring ◽  
Gorenstein Rings ◽  
Injective Modules ◽  
Flat Modules ◽  
Coherent Ring ◽  
Acyclic Complexes ◽  
Gorenstein Flat ◽  
Gorenstein Injective

For a given class of modules [Formula: see text], let [Formula: see text] be the class of exact complexes having all cycles in [Formula: see text], and dw([Formula: see text]) the class of complexes with all components in [Formula: see text]. Denote by [Formula: see text][Formula: see text] the class of Gorenstein injective R-modules. We prove that the following are equivalent over any ring R: every exact complex of injective modules is totally acyclic; every exact complex of Gorenstein injective modules is in [Formula: see text]; every complex in dw([Formula: see text][Formula: see text]) is dg-Gorenstein injective. The analogous result for complexes of flat and Gorenstein flat modules also holds over arbitrary rings. If the ring is n-perfect for some integer n ≥ 0, the three equivalent statements for flat and Gorenstein flat modules are equivalent with their counterparts for projective and projectively coresolved Gorenstein flat modules. We also prove the following characterization of Gorenstein rings. Let R be a commutative coherent ring; then the following are equivalent: (1) every exact complex of FP-injective modules has all its cycles Ding injective modules; (2) every exact complex of flat modules is F-totally acyclic, and every R-module M such that M+ is Gorenstein flat is Ding injective; (3) every exact complex of injectives has all its cycles Ding injective modules and every R-module M such that M+ is Gorenstein flat is Ding injective. If R has finite Krull dimension, statements (1)–(3) are equivalent to (4) R is a Gorenstein ring (in the sense of Iwanaga).

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