Cadenes de Sales discretes
1980; Autonomous University of Barcelona; Volume: 20; Linguagem: Catalão
10.5565/publmat_20180_19
ISSN2014-4350
Autores Tópico(s)Scheduling and Optimization Algorithms
ResumoThe Sales algebras are the substract of some positive implicational calculi .As a first aproximation to their representation we Study the Sales algebras that are discrete and linear .In this paper we present a caracteritzation of the finite Sales algebras and we give also an infinite discrete Sales algebra such that we can identify with it every linear infinite simple Sales algebra with a penultimate element .The most interes ting result is the first Theorem In it we show that certain elements of the Sales algebras generate finit linear subalgebras of them .Per álgebras de Sales (a .de.S .),veigi's12] , [4],entenem una terna (A, .,u)amb A un conjunt, .una operació binaria definida en A, i u un element distingit de A(operació 0-aria), tal que per tot a,b ;c E A, satisfá : 1 .-a.a= u 2 .-a.b= b .a= u , implica a = b 3 .-a.u= u 4 .-a.(b.c)= b .(a.c)S .-(a.b).((c.a).(c.b))= u 6 .-(a.b).b= (b .a).a(Sales [31 ) Es a dir, (A, .,u)és un algebra d-completa que satisfá 6 .A més(veigi's[2) (4)), la relació a!Gb si¡ a .b= u, és d'ordre i u n!és 1"element maxim ; és a dir,(A, .,u)es álgebra im1icativa .D'altra banda a v b = (a .b).bés el suprem de a i b i (A, .,v,u)és suprareticle d-complet(op .cit) .Quan (A,_-5) té element minim 0 ( [2] L4J ) , ales-
Referência(s)