If is a Tychonoff space, its ring of real-valued continuous functions. In this paper, we study non-essential ideals in . Let be a infinite cardinal, then is called -Kasch (resp. -Kasch) space if given any ideal (resp. -ideal) with then is a non-essential ideal. We show that is an -Kasch space if and only if is an almost -space and is an -Kasch space if and only if is a pseudocompact and almost -space. Let denote the socle of . For a topological space with only...
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.
In this note we give a description of a morphism related to the structure of the canonical model of the Rees algebra R(I) of an ideal I in a local ring. As an application we obtain Ikeda's criteria for the Gorensteinness of R(I) and a result of Herzog-Simis-Vasconcelos characterizing when the canonical module of R(I) has the expected form.