ABSTRACT
Within a specified class, say C https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq695.tif"/> , of lattice-ordered algebraic structures, with a subclass Q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq696.tif"/> , a Q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq697.tif"/> -hull of an object A is a minimal essential extension of A in Q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq698.tif"/> . We shall consider classes (nontrivial, isomorphism-closed and full subcategories) for which each object A of C https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq699.tif"/> has a Q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq700.tif"/> -hull Ac↪qA with the (strong) property that each homomorphism of A to a Q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq701.tif"/> -object extends uniquely over qA; we call such a Q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072652/662509b9-dada-4fff-9fc1-ac3384cba138/content/eq702.tif"/> and its associated hulls, quasi-algebraic. We shall prove this:
