Introduction In the theory of groups, the important concepts of Abelian group, solvable group, nilpotent group, the center of a group and centraliz-ers, are all defined from the binary operation [x, y] = x −1 y −1 xy. Each of these notions, except centralizers of elements, may also be defined in terms of the commutator of normal subgroups. The commutator… (More)
The Constraint Satisfaction Problem Dichotomy Conjecture of Feder and Vardi (1999) has in the last 10 years been profitably reformulated as a conjecture about the set SP fin (A) of subalgebras of finite Cartesian powers of a finite universal algebra A. One particular strategy, advanced by Dalmau in his doctoral thesis (2000), has confirmed the conjecture… (More)
Dedicated to my wife, Regina, with my everlasting love. ii ACKNOWLEDGMENTS I would like to express my gratitude to a number of people without whose support this thesis would not have been possible. I could not possibly mention all of them. First and foremost I would like to thank my advisor, Professor Ralph McKenzie. I would like to thank him for all the… (More)
An n-ary operation f : A n → A is called cyclic, if it is idempotent and f (a 1 , a an ∈ A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than |A|.
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… (More)
In this paper we study first-order definability in the lattice of equational theories of commutative semigroups. In a series of papers, J. Ježek, solving problems posed by A. Tarski and R. McKenzie, has proved, in particular , that each equational theory is first-order definable in the lattice of equational theories of a given type, up to automorphism, and… (More)
We prove that for any variety V, the existence of an edge-term (defined in ) and Jónsson terms is equivalent to the existence of a near-unanimity term. We also characterize the idempotent Maltsev conditions which are defined by a system of linear absorption equations and which imply congruence distributivity.
To the memory of my father, Francesco. To my newborn nephew and godson, wishing he will share with his grandad much more than the bare name. Acknowledgements Most of the people who read a doctoral dissertation are academics. Then, as it often understandably happens, they may underestimate its importance for the author. A Ph.D. thesis represents a sort of… (More)