Geodesic
On Plücker properties of rings
Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 517-528 
G. B. Kleiner. On Plücker properties of rings. Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 517-528. http://geodesic.mathdoc.fr/item/SM_1971_13_4_a1/
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     author = {G. B. Kleiner},
     title = {On {Pl\"ucker} properties of rings},
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     volume = {13},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_4_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Questions are considered of decomposability of $m$-vectors from $\Lambda^m(A^n)$, where $A$ is a commutative ring with $1$, and $A^n$ is the direct sum of $n$ copies of $A$. Let $A$ be a Krull ring. We shall denote by $\operatorname{div}\omega$ the greatest common divisor of the coordinates of the $m$-vector $\omega\in\Lambda^m(A^n)$. For the case where the $\operatorname{div}\omega$ is square-free in terms of the $A$-module $K_\omega=\{x\in A^n:x\land\omega=0\}$ necessary and sufficient conditions are given for decomposability of $\omega$. A characterization of factorial Plücker rings is stated, i.e. rings in which for arbitrary $n>m\geqslant2$ every $m$-vector of $\Lambda^m(A^n)$ which satisfies the Plücker condition is decomposable. Bibliography: 8 titles.

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[8] N. Bourbaki, Algebre commutative, Chap. 7, Hermann, Paris, 1965 | MR