We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Duality and syzygies for semimodules over numerical semigroups.
- Authors
Moyano-Fernández, Julio; Uliczka, Jan
- Abstract
Let $$\Gamma =\langle \alpha , \beta \rangle $$ be a numerical semigroup. In this article we consider the dual $$\Delta ^*$$ of a $$\Gamma $$ -semimodule $$\Delta $$ ; in particular we deduce a formula that expresses the minimal set of generators of $$\Delta ^*$$ in terms of the generators of $$\Delta $$ . As applications we compute the minimal graded free resolution of a graded $${\mathbb {F}}[t^{\alpha },t^{\beta }]$$ -submodule of $${\mathbb {F}}[t]$$ , and we investigate the structure of the selfdual $$\Gamma $$ -semimodules, leading to a new way of counting them.
- Subjects
DUALITY theory (Mathematics); SYZYGIES (Mathematics); SEMIGROUPS (Algebra); FREE resolutions (Algebra); COMMUTATIVE algebra; POLYNOMIAL rings
- Publication
Semigroup Forum, 2016, Vol 92, Issue 3, p675
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-015-9700-x