A note on D. Quillen’s paper: ‘‘Projective modules over polynomial rings” (Invent. Math. {\bf 36} (1976), 167–171)

Projective modules over polynomial rings and dynamical Gröbner bases

On Projective Modules over Semi-hereditary Rings

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...

Modules over Differential Polynomial Rings

This note announces a number of results on the structure of differential modules over differential rings, where differential ring means a ring with a family of derivations and differential module means a module having a family of operators compatible with the derivations of the ring. To fix notation, throughout the paper we let A denote an associative ring, M = AM an 4-module, k the correspondi...

On modules over Laurent polynomial rings

A finitely generated Λ = Z[t, t]-module without Z-torsion is determined by a pair of sub-lattices of Λ. Their indices are the absolute values of the leading and trailing coefficients of the order of the module. This description has applications in knot theory. MSC 2010: Primary 13E05, 57M25.

Note on Star Operations over Polynomial Rings

This paper studies the notions of star and semistar operations over a polynomial ring. It aims at characterizing when every upper to zero in R[X] is a ∗-maximal ideal and when a ∗-maximal ideal Q of R[X] is extended from R, that is, Q = (Q ∩ R)[X] with Q ∩R 6= 0, for a given star operation of finite character ∗ on R[X]. We also answer negatively some questions raised by Anderson-Clarke by const...