Finitely generated modules

2011 ◽  
pp. 229-241
Author(s):  
Theodore G. Faticoni
Keyword(s):  
Finitely Generated ◽  
Finitely Generated Modules

scholarly journals Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras

2016 ◽  
Vol 23 (04) ◽  
pp. 701-720 ◽  
Author(s):  
Xiangui Zhao ◽  
Yang Zhang
Keyword(s):  
Computational Method ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Polynomial Algebras ◽  
Ore Extensions ◽  
Basis Method ◽  
Finitely Generated Modules ◽  
Kirillov Dimension

Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.

Finitely generated modules over valuation rings

1984 ◽  
Vol 12 (15) ◽  
pp. 1795-1812 ◽  
Author(s):  
Luigi Salce ◽  
Paolo Zanardo
Keyword(s):  
Finitely Generated ◽  
Valuation Rings ◽  
Finitely Generated Modules

scholarly journals Maximal depth property of finitely generated modules

2018 ◽  
Vol 17 (11) ◽  
pp. 1850202 ◽  
Author(s):  
Ahad Rahimi
Keyword(s):  
Local Ring ◽  
Finitely Generated ◽  
Noetherian Local Ring ◽  
Maximal Depth ◽  
Finitely Generated Modules ◽  
Associated Prime

Let [Formula: see text] be a Noetherian local ring and [Formula: see text] a finitely generated [Formula: see text]-module. We say [Formula: see text] has maximal depth if there is an associated prime [Formula: see text] of [Formula: see text] such that depth [Formula: see text]. In this paper, we study finitely generated modules with maximal depth. It is shown that the maximal depth property is preserved under some important module operations. Generalized Cohen–Macaulay modules with maximal depth are classified. Finally, the attached primes of [Formula: see text] are considered for [Formula: see text].

scholarly journals A note on thick subcategories of stable derived categories

2013 ◽  
Vol 212 ◽  
pp. 87-96
Author(s):  
Henning Krause ◽  
Greg Stevenson
Keyword(s):  
Derived Categories ◽  
Derived Category ◽  
Complete Intersections ◽  
Line Bundles ◽  
Finitely Generated ◽  
Exact Category ◽  
Coherent Sheaves ◽  
Noetherian Scheme ◽  
Finitely Generated Modules ◽  
Local Complete Intersections

AbstractFor an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection, we classify thick subcategories of finitely generated modules over strict local complete intersections and produce generators for the category of coherent sheaves on a separated Noetherian scheme with an ample family of line bundles.

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