Geodesic
Algebraic interpretation of derivation axioms completeness
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 195-219.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FPM_2002_8_1_a15,
     author = {L. A. Pomortsev},
     title = {Algebraic interpretation of derivation axioms completeness},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {195--219},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a15/}
}
TY  - JOUR
AU  - L. A. Pomortsev
TI  - Algebraic interpretation of derivation axioms completeness
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2002
SP  - 195
EP  - 219
VL  - 8
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a15/
LA  - ru
ID  - FPM_2002_8_1_a15
ER  - 
%0 Journal Article
%A L. A. Pomortsev
%T Algebraic interpretation of derivation axioms completeness
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2002
%P 195-219
%V 8
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a15/
%G ru
%F FPM_2002_8_1_a15
L. A. Pomortsev. Algebraic interpretation of derivation axioms completeness. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 195-219. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a15/

[1] Meier D., Teoriya relyatsionnykh baz dannykh, Mir, M., 1987

[2] Kon P., Universalnaya algebra, Mir, M., 1968 | MR