Cardinality of generating sets for modules over a commutative ring.
Chains of factorizations in weakly Krull domains
Characterizations of some rings with -projective, -(FP)-injective and -flat modules
Let be a commutative ring and a semidualizing -module. We investigate the relations between -flat modules and -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.
Cofiniteness and finiteness of local cohomology modules over regular local rings
Let be a commutative Noetherian regular local ring of dimension and be a proper ideal of such that . It is shown that the -module is -cofinite if and only if . Also we present a sufficient condition under which this condition the -module is finitely generated if and only if it vanishes.
Cofiniteness of torsion functors of cofinite modules
Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely generated R-module. It is shown that the R-modules are I-cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 1 or dim Supp(N) ≤ 2. This immediately implies that if I has dimension one (i.e., dim R/I = 1) then the R-modules are I-cofinite for all i,j ≥ 0. Also, we prove that if R is local, then the R-modules are I-weakly cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 2 or dim Supp(N) ≤ 3. Finally, it is shown that...
Cohen-Macaulayness of multiplication rings and modules
Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.
Comportement des de Bass dans les extensions plates
Condition d’Ischebeck-Auslander et condition de Serre
Conductive Integral Domains as Pullbacks.
Conservation des propriétés des fibres formelles d'un anneau semi-local noethérien par complétion adique
Conservation of the noetherianity by perfect transcendental field extensions.
Construction of a controller with a generalized linear immersion
Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.
Constructions of finitely generated submodules of constructively noetherian modules
Correction to: Maximal orders of global dimension and Krull dimension two.