Assis de Azevedo (auth.), Jorge Almeida, Gabriela Bordalo,'s Lattices, Semigroups, and Universal Algebra PDF

By Assis de Azevedo (auth.), Jorge Almeida, Gabriela Bordalo, Philip Dwinger (eds.)

ISBN-10: 1489926089

ISBN-13: 9781489926081

ISBN-10: 1489926100

ISBN-13: 9781489926104

This quantity includes papers which, for the main half, are according to talks given at a global convention on Lattices, Semigroups, and common Algebra that used to be held in Lisbon, Portugal through the week of June 20-24, 1988. The convention was once devoted to the reminiscence of Professor Antonio Almeida Costa, a Portuguese mathematician who drastically contributed to the improvement of th algebra in Portugal, at the 10 anniversary of his demise. the subjects of the convention replicate a few of his study pursuits and people of his scholars. the aim of the convention was once to collect prime specialists in Lattices, Semigroups, and common Algebra and to advertise a dialogue of contemporary advancements and tendencies in those parts. All 3 fields have grown swiftly over the last few a long time with various levels of interplay. Lattice idea and common Algebra have traditionally developed along with a wide overlap among the teams of researchers within the fields. extra lately, suggestions and ideas of those theories were used widely within the concept of semigroups. Conversely, a few advancements in that region may possibly encourage extra advancements in common Algebra. however, strategies of semi workforce concept have clearly been hired within the examine of semilattices. a number of papers during this quantity complex on those interactions.

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Extra info for Lattices, Semigroups, and Universal Algebra

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Every finitely generated lattice of width at most 3 which does not contain any upward herringbone as a sublattice satisfies the A CC. That this result cannot be extended to width 4 or more was demonstrated by the following example in [18]: Figure 2. A christmas tree This 4-generated lattice of width 4 does not contain any herringbone as a sub/attice (although herringbones do occur as subposets). Recently, configurations of the previous type emerged in a quite different context, namely in the abstract characterization problem for lattices of equational theories and for congruence lattices of algebras possessing a binary term with a one-sided absorbing element and a one-sided neutral element (see [4], [15]).

Kilp, Commutative monoids all of whose principal ideals are projective. Semigroup Forum 6, 334-339 (1973). K. Shoji, Absolute flatness of the full transformation semigroups. J. Algebra 118 (1988), 477-486. Department of Mathematics Wilfrid Laurier University Waterloo, Ontario, Canada N2L 3C5 37 STAIRCASES AND A CONGRUENCE-THEORETICAL CHARACTERIZATION OF VECTOR SPACES Marcel Erne Abstract We study so-called staircases in lattices and certain related lattice properties which are weaker than distributivity but stronger than meetsemidistributivity.

Then the following statements are For every non-empty set r, Sr is a weakly flat right S-set. Every finitely generated left ideal of S is FD. For every x, YES, Sx n Sy is either a principal left ideal or empty. S is weakly left coherent. Proof. Since (4) implies (1) immediately, and (1) implies (2) implies (3) follows from Theorem 4, it remains to prove (3) implies (4). Assume (3), and refer to Proposition 6. Let {A, I , E r} be a non-empty family of weakly flat right S-sets. We show A and (a,)x = = n A, is weakly flat.

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Lattices, Semigroups, and Universal Algebra by Assis de Azevedo (auth.), Jorge Almeida, Gabriela Bordalo, Philip Dwinger (eds.)

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