8,269 research outputs found
Presentations of Topological Full Groups by Generators and Relations
We describe generators and defining relations for the commutator subgroup of
topological full groups of minimal subshifts. We show that the word problem in
a topological full group is solvable if and only if the language of the
underlying subshift is recursive.Comment: Some typos fixe
Artinian algebras and Jordan type
The Jordan type of an element of the maximal ideal of an Artinian
k-algebra A acting on an A-module M of k-dimension n, is the partition of n
given by the Jordan block decomposition of the multiplication map on
M. In general the Jordan type has more information than whether the pair
is strong or weak Lefschetz. We develop basic properties of the
Jordan type and their loci for modules over graded or local Artinian algebras.
We as well study the relation of generic Jordan type of to the Hilbert
function of . We introduce and study a finer invariant, the Jordan degree
type.
In our last sections we give an overview of topics such as the Jordan types
for Nagata idealizations, for modular tensor products, and for free extensions,
including examples and some new results. We as well propose open problems.Comment: 53 pages. Added results, examples for Jordan degree type (Section
2.4) and Jordan type and initial ideal (Section 2.5
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