Displaying similar documents to “Strongly prime alternative pairs with minimal inner ideals.”

On associated and attached prime ideals of certain modules

K. Divaani-Aazar (2001)

Colloquium Mathematicae

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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.

Intersections of minimal prime ideals in the rings of continuous functions

Swapan Kumar Ghosh (2006)

Commentationes Mathematicae Universitatis Carolinae

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A space X is called μ -compact by M. Mandelker if the intersection of all free maximal ideals of C ( X ) coincides with the ring C K ( X ) of all functions in C ( X ) with compact support. In this paper we introduce φ -compact and φ ' -compact spaces and we show that a space is μ -compact if and only if it is both φ -compact and φ ' -compact. We also establish that every space X admits a φ -compactification and a φ ' -compactification. Examples and counterexamples are given.