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Weak multiplication modules

Abdelmalek Azizi (2003)

Czechoslovak Mathematical Journal

In this paper we characterize weak multiplication modules.

When does the F -signature exist?

Ian M. Aberbach, Florian Enescu (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

We show that the F -signature of an F -finite local ring R of characteristic p > 0 exists when R is either the localization of an N -graded ring at its irrelevant ideal or Q -Gorenstein on its punctured spectrum. This extends results by Huneke, Leuschke, Yao and Singh and proves the existence of the F -signature in the cases where weak F -regularity is known to be equivalent to strong F -regularity.

When spectra of lattices of z -ideals are Stone-Čech compactifications

Themba Dube (2017)

Mathematica Bohemica

Let X be a completely regular Hausdorff space and, as usual, let C ( X ) denote the ring of real-valued continuous functions on X . The lattice of z -ideals of C ( X ) has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) β X precisely when X is a P -space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a d -ideal if whenever two elements have the same annihilator and...

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