12,627 research outputs found
Ray class invariants over imaginary quadratic fields
Let be an imaginary quadratic field of discriminant less than or equal to
-7 and be its ray class field modulo for an integer greater
than 1. We prove that singular values of certain Siegel functions generate
over by extending the idea of our previous work. These generators
are not only the simplest ones conjectured by Schertz, but also quite useful in
the matter of computation of class polynomials. We indeed give an algorithm to
find all conjugates of such generators by virtue of Gee and Stevenhagen
The structure of gauge-invariant ideals of labelled graph -algebras
In this paper, we consider the gauge-invariant ideal structure of a
-algebra associated to a set-finite,
receiver set-finite and weakly left-resolving labelled space
, where is a labelling map assigning
an alphabet to each edge of the directed graph with no sinks. Under the
assumption that an accommodating set is closed under taking
relative complement, it is obtained that there is a one to one correspondence
between the set of all hereditary saturated subsets of and the
gauge-invariant ideals of . For this, we
introduce a quotient labelled space arising
from an equivalence relation on and show the existence
of the -algebra generated by a
universal representation of . Also the
gauge-invariant uniqueness theorem for is
obtained.
For simple labelled graph -algebras
, where is the
smallest accommodating set containing all the generalized vertices, it is
observed that if for each vertex of , a generalized vertex is
finite for some , then is simple if
and only if is strongly cofinal and
disagreeable. This is done by examining the merged labelled graph
of and the common properties that
and
share
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