Lattices, Semigroups, and Universal AlgebraJorge Almeida, Gabriela Bordalo, Philip Dwinger This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions. |
Contents
| 1 | |
Some Examples of Distributive Ockham Algebras with De Morgan Skeletons | 21 |
Staircases and a CongruenceTheoretical Characterization of Vector Spaces | 39 |
Inverse Semigroups of Bicongruences on Algebras Particularly Semilattices | 59 |
The Complete Congruence Lattice of a Complete Lattice | 81 |
Arithmetical Aspects of Semigroup Embeddings | 101 |
Inverse Semigroups and Their Lattices of Inverse Subsemigroups | 115 |
Varieties of Algebras with No Nontrivial Finite Members | 129 |
Residually Small Varieties Revisited | 185 |
The Kernel of an Idempotent Separating Congruence on a Regular Semigroup | 203 |
Completely Regular Semigroups | 225 |
Survey of Global Semigroup Theory | 243 |
Generalized Power Series Rings | 271 |
Amalgamation in Pseudocomplemented Semilattices | 291 |
An Extension of the Schützenberger Product | 315 |
| 335 | |
Other editions - View all
Lattices, Semigroups, and Universal Algebra Jorge Almeida,Gabriela Bordalo,Philip Dwinger No preview available - 2013 |
Lattices, Semigroups, and Universal Algebra Jorge Almeida,Gabriela Bordalo,Philip Dwinger No preview available - 2013 |
Lattices, Semigroups, and Universal Algebra Jorge Almeida,Gabriela Bordalo,Philip Dwinger No preview available - 1990 |
Common terms and phrases
0-simple A)MM a₁ abelian Algebra Universalis Amer automorphism B₁ bands BC(A bijection biordered set Boolean chain combinatorial commutative complete congruence complete lattice completely regular completely regular semigroups component condition congruence lattice conjecture consider contains Corollary defined denote distributive lattice elements embedding equations equivalent example exists extraction monoid f₁ finite monoids finite semigroups free semigroup global semigroup theory Grätzer group kernel Hence homomorphism idempotent identity implies infinite inside factorial integers inverse semigroup inverse subsemigroups Jacobson ring K₁ Krull languages Lemma M₁ mapping Math modular morphism MS-algebra nilpotent nontrivial Ockham algebra operations permutation Petrich polynomial prime ideal problem Proc Proof properties Proposition proved pseudovariety regular semigroup relation residually small result S₁ satisfies Semigroup Forum semigroup rings semilattice simple semigroup structure subalgebra subdirectly irreducible subgroups subsemigroup subset subvariety Theorem Univ Universal Algebra variety