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Iterative differentiations in rings of unequal characteristic

Marilena Crupi, Gaetana Restuccia (2001)

Bollettino dell'Unione Matematica Italiana

Sia R un anello di caratteristica diseguale. Si stabiliscono formule generali per gli endomorfismi di una differenziazione F a o F c -iterativa di R , con c non zerodivisore di R. Tali formule sono note nel caso della caratteristica eguale.

Jung's type theorem for polynomial transformations of ℂ²

Sławomir Kołodziej (1991)

Annales Polonici Mathematici

We prove that among counterexamples to the Jacobian Conjecture, if there are any, we can find one of lowest degree, the coordinates of which have the form x m y n + terms of degree < m+n.

k -torsionless modules with finite Gorenstein dimension

Maryam Salimi, Elham Tavasoli, Siamak Yassemi (2012)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring. It is shown that the finitely generated R -module M with finite Gorenstein dimension is reflexive if and only if M 𝔭 is reflexive for 𝔭 Spec ( R ) with depth ( R 𝔭 ) 1 , and G- dim R 𝔭 ( M 𝔭 ) depth ( R 𝔭 ) - 2 for 𝔭 Spec ( R ) with depth ( R 𝔭 ) 2 . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for n 2 we give a characterization of n -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown...

Kaplansky classes

Edgar E. Enochs, J. A. López-Ramos (2002)

Rendiconti del Seminario Matematico della Università di Padova

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