FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 1, PAGES 195-219
L. A. Pomortsev
Abstract
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The operation
$(X \to Y) \blacktriangleright (Z \to V)
= X \cup (Z \setminus Y) \to (Y \cup V)$
is determined in the full set $\{X \to Y
\mid X,Y \subseteq R\}$
of F-dependences over a certain scheme $R$ .
Let $\Phi$ be an F-dependence, which follows from a set $F$
of F-dependences. We prove that
$\Phi = \Phi_1 \blacktriangleright \Phi_2
\blacktriangleright \ldots \blacktriangleright \Phi_k
\blacktriangleright W \cdot \mathbf{F2} \cdot \mathbf{B3}$
for some
$\Phi_1,\Phi_2,\ldots,\Phi_k \in F$ and
$W \subseteq R$ , where $\Phi_k
\blacktriangleright W = \Phi_k \blacktriangleright (W \to W)$ .
The unary operations $\cdot \mathbf{F2}$ and $\cdot \mathbf{B3}$
correspond to axioms of derivation
$\mathbf{F2}$ (completion) and $\mathbf{B3}$ (projectivity) pro tanto.
All articles are published in Russian.
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Last modified: July 5, 2002