Lattices, Semigroups, and Universal Algebra

ISBN-13: 9781489926104 / Angielski / Miękka / 2013 / 336 str.

Jorge Almeida; Gabriela Bordalo; Philip Dwinger

Opis

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.

Spis treści

The Join of the Pseudovariety J with Permutative Pseudovarieties.- On the Combinatorics of Free Algebras.- Some Examples of Distributive Ockham Algebras with De Morgan Skeletons.- Coherent Monoids.- Staircases and a Congruence-Theoretical Characterization of Vector Spaces.- Inverse Semigroups of Bicongruences on Algebras, Particularly Semilattices.- Finitely Presented Lattices: Continuity and Semidistributivity.- On the Structure of Partial Automorphism Semigroups.- The Complete Congruence Lattice of a Complete Lattice.- Random Products in Semigroups of Mappings.- Arithmetical Aspects of Semigroup Embeddings.- Semigroup Graded Rings and Jacobson Rings.- Inverse Semigroups and Their Lattices of Inverse Subsemigroups.- Varieties of Algebras with No Nontrivial Finite Members.- The Set of Quasi-Identities of an Algebra.- Relatively Prime Gröbner Bases and Reducibility of S-Polynomials.- Semigroups that are Factorial from Inside or from Outside.- Programs over Finite Semigroups: an Introduction.- Normal Semigroups of Partial Transformations, I.- Residually Small Varieties Revisited.- Semigroup Rings of Completely Regular Semigroups.- The Kernel of an Idempotent Separating Congruence on a Regular Semigroup.- Structural Theorems for Varieties of Bands.- Completely Regular Semigroups.- Survey of Global Semigroup Theory.- Generalized Power Series Rings.- The Degree of Invariancy of a Bicentrally Closed Clone.- Subsemigroups of Free Semigroups.- Amalgamation in Pseudocomplemented Semilattices.- MS-Algebras: a Survey.- An Extension of the Schützenberger Product.- Congruence Lattices of Finite Lattices as Concept Lattices.- Problem Session.- Participants.