Frobenius criteria of freeness and Gorensteinness

Criteria to Disprove Context-Freeness of Collage Languages

Collage grammars generate picture languages in a context-free way. The generating process is based on the replacement of atomic nonterminal items and can be seen as an adaptation of the notion of hyperedge replacement known from the area of context-free graph generation. While a pumping lemma holds for hyperedge replacement graph grammars and is quite useful to show that certain graph languages...

NEW CRITERIA FOR FREENESS IN ABELIAN GROUPS . H ( i )

A new criterion is established for an abelian group to be free. The criterion is in terms of an ascending chain of free subgroups and is dependent upon a new class of torsion-free groups. The result leads to the construction, for each positive integer n, of a group G of cardinality K that is not free but is X -free. A conjecture in infinitary logic concern71 n ing free abelian groups is also ve...

Gorensteinness of Invariant Subrings of Quantum Algebras

We prove Auslander-Gorenstein and GKdim-Macaulay properties for certain invariant subrings of some quantum algebras, the Weyl algebras, and the universal enveloping algebras of finite dimensional Lie algebras.

Continuity, freeness, and filtrations

The role played by continuous morphisms in propositional modal logic is investigated: it turns out that they are strictly related to filtrations and to suitable variants of the notion of a free algebra. We also employ continuous morphisms in the incremental construction of (standard) finitely generated free S4-algebras. This Technical Report reproduces the content of my talk given at the worksh...

Weighted Frobenius-Perron and Koopman operators