The search session has expired. Please query the service again.
Let R be a unital commutative ring and A a unital R-algebra. We introduce the category of E(A,R)-modules which is a natural extension of the category of E-modules. The properties of E(A,R)-modules are studied; in particular we consider the subclass of E(R)-algebras. This subclass is of special interest since it coincides with the class of E-rings in the case R = ℤ. Assuming diamond ⋄, almost-free E(R)-algebras of cardinality κ are constructed for any regular non-weakly compact cardinal κ > ℵ...
Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if . In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.
Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
Let be a local ring, an ideal of and a nonzero Artinian -module of Noetherian dimension with . We determine the annihilator of the top local homology module . In fact, we prove that
where denotes the smallest submodule of such that . As a consequence, it follows that for a complete local ring all associated primes of are minimal.
Let be a complete Noetherian local ring, an ideal of and a nonzero Artinian -module. In this paper it is shown that if is a prime ideal of such that and is not finitely generated and for each the -module is of finite length, then the -module is not of finite length. Using this result, it is shown that for all finitely generated -modules with and for all integers , the -modules are of finite length, if and only if, for all finitely generated -modules with and...
Let be an ideal of Noetherian local ring and a finitely generated -module of dimension . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to . Also we prove that for an arbitrary local ring (not necessarily complete), we have
In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring , which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincaré...
Let be a set of ideals of a commutative Noetherian ring . We use the notion of -closure operation which is a semiprime closure operation on submodules of modules to introduce the class of -Laskerian modules. This enables us to investigate the set of associated prime ideals of certain -closed submodules of local cohomology modules.
Currently displaying 41 –
60 of
60