All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 178

Showing per page

Cohen-Lenstra sums over local rings

Christian Wittmann (2004)

Journal de Théorie des Nombres de Bordeaux

We study series of the form ∑ M | Aut R ( M ) | - 1 | M | - u , where R is a commutative local ring, u is a non-negative integer, and the summation extends over all finite R -modules M , up to isomorphism. This problem is motivated by Cohen-Lenstra heuristics on class groups of number fields, where sums of this kind occur. If R has additional properties, we will relate the above sum to a limit of zeta functions of the free modules R n , where these zeta functions count R -submodules of finite index in R n . In particular we will show that...

Cohen-Macaulayness of multiplication rings and modules

R. Naghipour, H. Zakeri, N. Zamani (2003)

Colloquium Mathematicae

Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.

Cohomological dimension filtration and annihilators of top local cohomology modules

Ali Atazadeh, Monireh Sedghi, Reza Naghipour (2015)

Colloquium Mathematicae

Let denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration = M i i = 0 c , where c = cd(,M) and M i denotes the largest submodule of M such that c d ( , M i ) ≤ i . Some properties of this filtration are investigated. In particular, if (R,) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module H c ( M ) , namely A n n R ( H c ( M ) ) = A n n R ( M / M c - 1 ) . As a consequence, there exists an ideal of R such that A n n R ( H c ( M ) ) = A n n R ( M / H ⁰ ( M ) ) . This generalizes the main results...

Combinatoric of syzygies for semigroup algebras.

Emilio Briales, Pilar Pisón, Antonio Campillo, Carlos Marijuán (1998)

Collectanea Mathematica

We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.

Currently displaying 61 – 80 of 178