Date of Award


Document Type


Degree Name


Organizational Unit

College of Natural Science and Mathematics, Mathematics

First Advisor

Nikolaos Galatos

Second Advisor

Michael Kinyon

Third Advisor

Andrew Linshaw

Fourth Advisor

Mark Siemens

Fifth Advisor

Petr Vojtechovsky


Amalgamation, Axiomatization, Classification, Involutive, Subvarieties, Unilinear residuated lattices


We characterize all residuated lattices that have height equal to 3 and show that the variety they generate has continuum-many subvarieties. More generally, we study unilinear residuated lattices: their lattice is a union of disjoint incomparable chains, with bounds added. We give the characterization of all unilinear residuated lattices. By presenting the constructions and axiomatizations for different classes of unilinear residuated lattices, we conclude that the study of unilinear residuated lattices can be reduced to the study of the ⊤-unital ones. Using the classification of unilinear residuated lattices, the idempotent unilinear residuated lattices are studied and amalgamation property and strong amalgamation properties are proved or disproved, depending on if there are extra constants in the language. We give two general constructions of ⊤-unital unilinear residuated lattices, provide an axiomatization and a proof-theoretic calculus for the variety they generate, and prove the finite embeddability property for various subvarieties. Finally, we study the involutive unilinear residuated lattices and give the characterization of a class of commutative 1-involutive compact unilinear residuated lattices. We present some open problems and future work at the end.

Copyright Date


Copyright Statement / License for Reuse

All Rights Reserved
All Rights Reserved.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Xiao Zhuang


Received from ProQuest

File Format



English (eng)


149 pgs

File Size

779 KB



Available for download on Thursday, September 12, 2024