Linear forms on free modules over certain local ring
Local Cohomology and the Cousin Complex for a Commutative Noetherian Ring.
Loewy series of modules.
Matrix of ℤ-module1
In this article, we formalize a matrix of ℤ-module and its properties. Specially, we formalize a matrix of a linear transformation of ℤ-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free ℤ-module V, determinant of its Gramian matrix is constant regardless of selection of its basis. ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattices [22]...
Minimal injective resolutions with applications to dualizing modules and Gorenstein modules
Modules de Gorenstein et modules canoniques
Modules of piecewise polynomials and their freeness.
Modules projectifs universels.
Moduln, die in jeder Erweiterung ein Komplement haben.
Morita-injektive Moduln über kommutativen Dedekind-Ringen.
Non-free Projective Modules Over IH[X, Y] and Stable Bundles Over IP2(...).
Normal and tangential flatness.
Note on projective modules.
On a generalization of a Prüfer-Kaplansky-Procházka theorem
On a generalization of de Rham lemma
Let be a free module over a noetherian ring. For , let be the ideal generated by coefficients of . For an element with , if , there exists such that .This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.
On chains of free modules over valuation domains
On Gaussian polynomials and content ideal.
On locally divided integral domains and CPI-overrings.
On Projective Modules.
On Projective Resolutions of Frobenius Algebras and Gorenstein Rings.