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Tue, 19 Dec 2017 09:28:00 +0100
Tue, 19 Dec 2017 09:28:00 +0100

Two instances of duality in commutative algebra
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/5111
In this thesis we address two instances of duality in commutative algebra.
In the first part, we consider value semigroups of non irreducible singular algebraic curves
and their fractional ideals. These are submonoids of Z^n closed under minima, with a conductor and which fulfill special compatibility properties on their elements. Subsets of Z^n
fulfilling these three conditions are known in the literature as good semigroups and their ideals, and their class strictly contains the class of value semigroup ideals. We examine
good semigroups both independently and in relation with their algebraic counterpart. In the combinatoric setting, we define the concept of good system of generators, and we
show that minimal good systems of generators are unique. In relation with the algebra side, we give an intrinsic definition of canonical semigroup ideals, which yields a duality
on good semigroup ideals. We prove that this semigroup duality is compatible with the CohenMacaulay duality under taking values. Finally, using the duality on good semigroup ideals, we show a symmetry of the PoincarĂ© series of good semigroups with special properties.
In the second part, we treat Macaulayâ€™s inverse system, a onetoone correspondence
which is a particular case of Matlis duality and an effective method to construct Artinian kalgebras with chosen socle type. Recently, Elias and Rossi gave the structure of the inverse system of positive dimensional Gorenstein kalgebras. We extend their result by establishing a onetoone correspondence between positive dimensional level kalgebras and certain submodules of the divided power ring. We give several examples to illustrate
our result.
Laura Tozzo
doctoralthesis
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/5111
Tue, 19 Dec 2017 09:28:00 +0100

Tropical Geometry in Singular
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/4169
Yue Ren
doctoralthesis
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/4169
Wed, 09 Sep 2015 10:34:35 +0200