The semigroup structure of left Clifford semirings. (Q1421085)

A left zero band semiring is a semiring whose additive reduct is a left zero band and whose multiplicative reduct is a band. A left ring is the direct product of a left zero band semiring and a ring, and a left Clifford semiring is a distributive lattice of left rings. This paper gives several structural characteristics of left Clifford semirings and investigates a construction which yields a special class of such left Clifford semirings. The construction under consideration goes by the name ``strong distributive lattice of left rings''.