Varieties of Residuated Lattices

ACKNOWLEDGMENTS This thesis wouldn't have been possible without the help and support of certain people. I could not possibly itemize my gratitude in detail, but I would like to mention some of the most important names. First and foremost, I would like to thank my advisor, Constantine Tsinakis, for introducing me to the subject of residuated lattices, and for his guidance and advice. Despite his busy schedule and administrative duties, he would always set aside plenty of time to discuss mathematics with me and patiently monitor my attempts to do research. He has been most helpful in balancing between suggesting new problems and research directions on the one hand, and encouraging independence on the other. A major part of this thesis is joint research with him and all of my work has been influenced by his comments and suggestions. I would also like to express my gratitude to my advisor for enlightening me regarding some of the other necessary traits of being a mathematician, including engaging presentation techniques and proper proposal writing. I would like to thank my co-advisor Peter Jipsen for his immeasurable contributions to my research and to this thesis. During his two-year visit at Vanderbilt University, I had the opportunity to have many long discussions and to engage in joint research with him. Even though not a member of my committee, he has truly been a second advisor for me, and a lot of the work in my dissertation is due to his suggestions and remarks. Peter has also been a good friend and it is always a pleasure and an intellectual stimulus to meet with him-even since his departure from Vanderbilt. I am very grateful to my committee members. In particular, I was privileged to attend many of Ralph McKenzie's seminars on interesting topics of mathematics, to take my first graduate course in Universal Algebra from Steven Tschantz and to take a special topics course offered by Jonathan Farley. I would also like to thank Alan Peters for agreeing to be the extra-departmental member of my Ph.D. committee, and Professors Matthew Gould and Mark Sapir of Vanderbilt University for the interesting algebra courses that they offered. I was fortunate to collaborate with Professors Steve Seif and James Raftery, to whom I am grateful for the helpful discussions we have had. During my study in Vanderbilt University, I was lucky to be surrounded by excellent fellow graduate …