Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Yves Lequain"'
Autor:
Yves Lequain
Publikováno v:
Journal of Pure and Applied Algebra. 215(4):531-545
Let K be a field of characteristic zero, n≥1 an integer and An+1=K[X,Y1,…,Yn]〈∂X,∂Y1,…,∂Yn〉 the (n+1)th Weyl algebra over K. Let S∈An+1 be an order-1 differential operator of the type S=∂X+∑i=1n(aiYi+bi)∂Yi+∑i=1ngi with ai,b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c30f4fa1e068547e9c3b8e1e8a5c3dc
Autor:
Yves Lequain
Publikováno v:
Journal of Algebra. 319:2979-2993
We show that: (1) If ( G 1 , O 1 ) is a finitely generated divisibility group that is not lattice ordered and if ( G 2 , O 2 ) is a divisibility group such that Card ( G 2 ) > Card ( R ) , then the product ( G 1 , O 1 ) × ( G 2 , O 2 ) is not a divi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4e79b70801bf50ecff3482aa49f15e15
https://doi.org/10.1016/j.jalgebra.2007.07.020
https://doi.org/10.1016/j.jalgebra.2007.07.020
Autor:
Yves Lequain
Publikováno v:
Journal of Pure and Applied Algebra. 212:801-807
Let K be a field of characteristic zero, d a derivation of K [ X ; Y 1 , … , Y n ] of the type d = ∂ X + ∑ i = 1 n ( a i Y i + b i ) ∂ Y i with a i , b i ∈ K [ X ] for every i . We characterize the property “ d is a simple derivation of K
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e2dbec3a940798d912e731c104baa348
https://doi.org/10.1016/j.jpaa.2007.07.012
https://doi.org/10.1016/j.jpaa.2007.07.012
Publikováno v:
Glasgow Mathematical Journal. 47:269-285
We prove that if the order-one differential operator $S=\partial_1 + \sum_{i=2}^{n} \beta_i\partial_i + \gamma$ , with $\beta_i,\gamma \in K[x_1,\ldots,x_n]$ , generates a maximal left ideal of the Weyl algebra $A_n(K)$ , then $S$ does not admit any
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9481888d6d4d8a8cbe93fac5e47923cc
https://doi.org/10.1017/s001708950500248x
https://doi.org/10.1017/s001708950500248x
Publikováno v:
Journal of the London Mathematical Society. 68:615-630
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d883392b5fec30d3dcfae203d3f939b4
https://doi.org/10.1112/s0024610703004708
https://doi.org/10.1112/s0024610703004708
Publikováno v:
Journal of Algebra. 245(1):161-181
Let D be an integral domain. Two nonzero elements x, y ∈ D are v-coprime if (x) ∩ (y) = (xy). D is an almost-GCD domain (AGCD domain) if for every pair x, y ∈ D, there exists a natural number n = n(x, y) such that (xn) ∩ (yn) is principal. We
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7a393d194d8288f40f5248b5b521af9
Publikováno v:
Proceedings of the American Mathematical Society. 130:15-21
The conjectures of Zariski-Lipman and of Nakai are still open in general in the class of rings essentially of finite type over a field of characteristic zero. However, they have long been known to be true in dimension one. Here we give counterexample
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4d3c7491ae574d3678cdc2fa8f38f457
https://doi.org/10.1090/s0002-9939-01-05983-4
https://doi.org/10.1090/s0002-9939-01-05983-4
Publikováno v:
Journal of Algebra. 211:736-753
We establish an algorithm that, up to isomorphism, determines all the divisibility orders of Z n and describes them in terms of the archimedean total orders of Z i , 1 ≤ i ≤ n .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eb9d6a0f0bf8e278ed3266c3fb5ed01f
https://doi.org/10.1006/jabr.1998.7625
https://doi.org/10.1006/jabr.1998.7625
Publikováno v:
Journal of Pure and Applied Algebra. 79(1):45-50
Let R be a commutative reduced, Z-torsion free ring. Let d and δ be two locally nilpotent derivations of R which commute, a an element of R. We prove that the derivation ad + δ is locally nilpotent if and only if d(a) = 0.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd03229d0440be09ff4410e694be8533