JP Journal of Algebra, Number Theory and Applications
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Abstract: Let R
be a right weakly regular (r.w.r.) ring; i.e., every right ideal of R
is idempotent. Characterizations are given for r.w.r. rings in terms of a strong
semilattice decomposition for the semigroup of
all right ideals of the ring. The index set semilattice is shown to be
isomorphic to the semigroup of
all ideals of R. Connections are given between such decomposition and the minimal
and maximal right ideals of R.
Keywords and phrases: right weakly regular ring, band, strong semilattice decomposition, semilattice.
