It is
well
known
that
two-terminal
switching
circuits
may
be
represented
by
boolean
formulas.
Thus
the
study
of
certain
switching
circuit
problems
leads
to
the
study of
free
boolean
algebras,
in
particular
to
the
free
boolean
algebra
on
a
countably
infinite
set
of
generators.
An
abstract
characterization
of
this
algebra...
In this thesis we investigate the extension of certain theorems
of additive number theory to three algebraic systems. A generalization
of a theorem by Cauchy and Davenport on the cardinality of the
sum of two sets of residue classes is given. We obtain and compare
estimates for the order of...