An m-domain ring is a ring such that, for every element
, there exists a central idempotent
such that
,
and, if
is an idempotent such that
, then
. The multiplicative semigroup of an m-domain ring is a D-semigroup (with the unary operation
).
Given an m-domain ring , we can decompose it into an inverse system of pairwise disjoint right-cancellative D-semigroups with identities over the set of idempotent elements of
. In the talk, the following results on this decomposition will be presented.
First, the strong semilattice of D-semigroups obtained from this inverse system is the multiplicative D-semigroup of the ring .
Second, let
be an inverse system of pairwise disjoint right-cancellative D-semigroups with identities
over some lower semilattice
. If the strong semilattice of D-semigroups obtained from the inverse system
is the multiplicative D-semigroup of some m-domain ring
, then the inverse system
is the decomosition of the m-domain ring
.