Abstract:

By utilizing the generalized ρ-Green relations on semigroups, L^ρC-regular semigroups are researched. Some equivalent conditions for L^ρC-regular semigroups are proved, a semigroup is an L^ρC-regular semigroup if and only if it is a strong semilattice of Lcancellative monoids.

Key words:  ρ-Green relation; homomorphism; L^ρC-regular semigroup; semilattice decomposition