id: 04130441
dt: j
an: 04130441
au: Di Nola, Antonio; Lettieri, Ada
ti: Relation equations in residuated lattices.
so: Rend. Circ. Mat. Palermo, II. Ser. 38, No.2, 246-256 (1989).
py: 1989
pu: Circolo Matematico di Palermo, Palermo; Springer, Milano
la: EN
cc: 
ut: complete lattice; right residuated multiplication; Brouwerian lattice;
    relational equation
ci: 
li: doi:10.1007/BF02843997
ab: Let L be a complete lattice endowed with an order-preserving right
    residuated multiplication $\cdot$; in particular, if this
    multiplication is the lattice-theoretical meet, then L is a Brouwerian
    lattice. Let further X and Y be two nonempty sets. The set
    $R(L)=\{A\vert$ A: $X\times Y\to L\}$ of L-relations from X to Y is
    equipped with the pointwise order induced by the order of L and with
    the following multiplication: if $A,A’\in R(L)$ then $A\cdot A’$ is
    defined by $(A\cdot A’)(x,y)=\bigvee\sb{z\in L}A(x,z)\cdot
    A’(z,y)$. The authors point out that all results known in the
    literature about the relational equation $A\cdot X=B$ are in fact valid
    within the general framework defined above.
rv: S.Rudeanu