Variety generated by conical residuated lattice-ordered idempotent monoids

Abstract

In this paper, we study the variety generated by conical idempotent residuated lattices. After obtaining some properties of conical idempotent residuated lattices, we establish a chain decomposition theorem for conical idempotent residuated lattices and give an equational basis for the variety. It is proved that the variety has the finite embeddability property. It is also proved that the semigroup reduct of a semiconical idempotent residuated lattice is a regular band.