Necessary conditions for the existence of dualizing complexes in commutative algebra

1979 ◽  
pp. 213-229 ◽  
Author(s):  
Rodney Y. Sharp
Keyword(s):  
Commutative Algebra ◽  
Necessary Conditions ◽  
Dualizing Complexes

On Grothendieck's local duality theorem

1979 ◽  
Vol 85 (3) ◽  
pp. 431-437 ◽  
Author(s):  
M. H. Bijan-Zadeh ◽  
R. Y. Sharp
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Noetherian Ring ◽  
Duality Theorem ◽  
Great Emphasis ◽  
Triangulated Category ◽  
Elementary Approach ◽  
Commutative Noetherian Ring ◽  
Local Duality ◽  
Dualizing Complexes

In (11) and (12), a comparatively elementary approach to the use of dualizing complexes in commutative algebra has been developed. Dualizing complexes were introduced by Grothendieck and Hartshorne in (2) for use in algebraic geometry; the approach to dualizing complexes in (11) and (12) differs from that of Grothendieck and Hartshorne in that it avoids use of the concepts of triangulated category, derived category, and localization of categories, and instead places great emphasis on the concept of quasi-isomorphism of complexes of modules over a commutative Noetherian ring.

Dualizing complexes for commutative Noetherian rings

1975 ◽  
Vol 78 (3) ◽  
pp. 369-386 ◽  
Author(s):  
Rodney Y. Sharp
Keyword(s):  
Local Ring ◽  
Commutative Algebra ◽  
Present Author ◽  
Partial Solution ◽  
Noetherian Rings ◽  
Finitely Generated ◽  
Injective Dimension ◽  
Noetherian Local Ring ◽  
Dualizing Complexes

The theory of dualizing complexes of Grothendieck and Hartshorne ((5), chapter v) has turned out to be a useful tool even in commutative algebra. For instance, Peskine and Szpiro used dualizing complexes in their (partial) solution of Bass's conjecture concerning finitely-generated (f.-g.) modules of finite injective dimension over a Noetherian local ring ((7), chapitre I, §5); and the present author first obtained the results in (9) by using dualizing complexes.

Czech National Awareness in Moravia in the Revolutionary Years 1848/1849

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
František Čapka
Keyword(s):  
Nineteenth Century ◽  
Necessary Conditions ◽  
Cultural Contact ◽  
Significant Change ◽  
Mutual Relations ◽  
High Degree

AbstractThis study focuses on the process of the gradual shaping of Czech national awareness in Moravia from the beginning of the nineteenth century onwards when the necessary conditions for the development of improved mutual relations between the Czech (Slavic) population in the two Lands of the Czech Crown -Bohemia and Moravia - were slowly being formed. Moravia faced a number of handicaps to the development of a national revival in comparison with Bohemia, the most significant of which was the relatively high degree of Germanisation of the land. A change to the image of Moravia came in the revolutionary years 1848/1849, when Czech national awareness spread to broader sections of society in Moravia. The view of Bohemia held by the Moravians underwent significant change and a period of increasingly intensive political and cultural contact between the two lands arose.

SOCIAL PROTECTION IS A GUARANTEE OF FAMILY UNITY

2020 ◽  
Vol 7 (3) ◽  
pp. 89-96
Author(s):  
Dilbar Karshieva ◽  
Keyword(s):  
Social Protection ◽  
Necessary Conditions ◽  
Family Members ◽  
The State ◽  
The Military ◽  
Family Unity

This article demonstrates the great attention and care paid by the state to the military and their families in our country.Social protection of families of military men consists in creating necessary conditions for family members to develop and demonstrate their abilities in socio-economic, cultural, medical and other spheres.

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