Let be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of . The intersection of essential weak ideal in is also studied.
Primary and secondary functors have been introduced in [2] and applied to extend some results concerning asymptotic prime ideals. In this paper, the theory of primary and secondary functors is developed and examples of non-exact primary and non-exact secondary functors are presented. Also, as an application, the sets of associated and of attached prime ideals of certain modules are determined.
Let be an integral domain with the quotient field , an indeterminate over and an element of . The Bhargava ring over at is defined to be . In fact, is a subring of the ring of integer-valued polynomials over . In this paper, we aim to investigate the behavior of under localization. In particular, we prove that behaves well under localization at prime ideals of , when is a locally finite intersection of localizations. We also attempt a classification of integral domains ...
We consider the annihilator of certain local cohomology modules. Moreover, some results on vanishing of these modules will be considered.
The dual of a Gorenstein module is called a co-Gorenstein module, defined by Lingguang Li. In this paper, we prove that if R is a local U-ring and M is an Artinian R-module, then M is a co-Gorenstein R-module if and only if the complex is a minimal flat resolution for M when we choose a suitable triangular subset on R̂. Moreover we characterize the co-Gorenstein modules over a local U-ring and Cohen-Macaulay local U-ring.
In this paper, we use a characterization of -modules such that to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting to be the local cohomology functor of with respect to the maximal ideal where is the Krull dimension of .