Back to Search
Start Over
On the deviation and the type of certain local Cohen–Macaulay rings and numerical semigroups
- Source :
- Journal of Algebra. 478:397-409
- Publication Year :
- 2017
- Publisher :
- Elsevier BV, 2017.
-
Abstract
- In J. Herzog and E. Kunz (1973) [6] it was shown that for any pair ( d , t ) ∈ N × N + with ( d , t ) ≠ ( 1 , 1 ) there exists a local Cohen–Macaulay ring R having deviation d ( R ) = d and type t ( R ) = t . By E. Kunz (1974) [7] the case d ( R ) = 1 , t ( R ) = 1 cannot occur. In this paper certain Cohen–Macaulay rings are studied for which there are close relations between deviation, type and embedding dimension. Similar relations for other classes of local rings have been proved in the recent paper by L. Sharifan (2014) [15] . Our relations will be applied to numerical semigroups (or equivalently monomial curves) and lead also to some further cases, generalizing E. Kunz (2016) [8] with ring-theoretic proofs, in which a question of H. Wilf (1978) [16] has a positive answer.
- Subjects :
- Discrete mathematics
Monomial
Ring (mathematics)
Algebra and Number Theory
Mathematics::Commutative Algebra
010102 general mathematics
Dimension (graph theory)
Local ring
010103 numerical & computational mathematics
Type (model theory)
01 natural sciences
Combinatorics
Cohen–Macaulay ring
Numerical semigroup
Embedding
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 00218693
- Volume :
- 478
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra
- Accession number :
- edsair.doi...........06f7575398ae18f5cb578a8be639e596