| Allen Kent, Harold Lancour, Jay E. Daily - Language Arts & Disciplines - 1979 - 576 pages
...also true in lattices. A lattice is said to be distributive if for all elements x, y, and z in it, **x A (y V z) = (x A y) v (x A z).** It turns out that this property is equivalent to the "dual" property that x V 0> A z) = (* V y) A (*... | |
| Kichoon Yang - Mathematics - 1988 - 174 pages
...Definition. Let (S, <, V, A) = S be a lattice. i) S is said to be distributive if for every x, y, z 6 S, **x A (y V z) = (x A y) V (x A z)** and x V (y A z) = (x V y) A (x V z) (the two conditions are in fact equivalent), ii) xe S is called... | |
| Vi͡acheslav Nikolaevich Saliĭ - Mathematics - 1988 - 113 pages
...(y V z) = (x A y) V (x A z), which is called the distributive law. Note that in any lattice we have **x A (y V z) > (x A y) V (x A z),** so that the meaning of the distributive law is really the declaration of the reverse inequality. 2.... | |
| Michel Marchand - 1989 - 499 pages
...totalement ordonné est un treillis distributif. 12. Soit L un treillis tel que: Vj-, y, z € L : **x A (y V z) = (x A y) V (x A z).** Montrer que: Vx, y, z,€ L : z V (y A z) = (x V y) A (* V z). 13. Montrer que le produit de deux treillis... | |
| Michael S. Paterson - Computers - 1990 - 780 pages
...automata. Recall that a Scott— domain (D,<) is distributive, if for any x,y,z 6 D such that y V z exists, **x A (y V z) = (x A y) V (x A z).** Then a dl— domain is a distributive finitary Scott-domain. Dl— domains have been much studied in... | |
| Saunders MacLane, Ieke Moerdijk - Mathematics - 1992 - 627 pages
...= x A y (or, equivalently, y = x V y). A distributive lattice L is a lattice in which the identity **x A (y V z) = (x A y) V (x A z)** (2) holds for all x, y, and z. This identity implies the dual distributive law x\I(yAz) = (xVy) A(xVz).... | |
| Roy L. Crole - Computers - 1993 - 335 pages
...aid the manipulation of meets and joins. Let X be a lattice. Then X is distributive if it satisfies **x A (y V z) = (x A y) V (x A z)** for all x, y, z in X. X is called modular if x < z implies x V (y A z) = (x V y) A z. REMARK 1.3.18... | |
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