Enlargements of Quantales

Abstract

A bstract In this paper, we study the enlargements of quantales. We prove three main results. First, if Q is a factorizable quantale, then any matrix quantale over Q is an enlargement of Q ; second, any unital Rees matrix quantale over a quantale Q with an identity is an enlargement of Q ; third, two quantales are Morita equivalent if and only if they have a joint enlargement. To prove these theorems, we use quantale matrices and modules and Morita contexts of quantales. Our main theorems and their proofs are parallel to those known for idempotent rings.