  Let $S$ be a discrete abelian semigroup with unit and concellations and
$\widehat {S}$ the semigroup of semicharacters of $S$. We shaw that the strong
boundary and the Shilov boundary of the algebra of generalized analytic
functions defined on $\widehat {S}$ are unions of some maximal subgroups of
$\widehat {S}$. We shaw also that the both boundaries coincide with the
character group of $S$ if $S$ does not contain nontrivial simple ideals. In the
last case the Gelfand spectrum of the algebra under consideration is
calculated.
