The Structure of Semiconic Idempotent Commutative Residuated Lattices

Abstract

In this paper, we study semiconic idempotent commutative residuated lattices. After giving some properties of such residuated lattices, we obtain a structure theorem for semiconic idempotent commutative residuated lattices. As an application, we make use of the structure theorem to prove that the variety of strongly semiconic idempotent commutative residuated lattices has the amalgamation property.

Keywords

• residuated lattices
• idempotent semigroup
• chain
• construction
• amalgamation