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Strongly fixed ideals in C ( L ) and compact frames

A. A. Estaji, A. Karimi Feizabadi, M. Abedi (2015)

Archivum Mathematicum

Let C ( L ) be the ring of real-valued continuous functions on a frame L . In this paper, strongly fixed ideals and characterization of maximal ideals of C ( L ) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C ( L ) , is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than...

Strongly rectifiable and S-homogeneous modules

Libuše Tesková (2000)

Discussiones Mathematicae - General Algebra and Applications

In this paper we introduce the class of strongly rectifiable and S-homogeneous modules. We study basic properties of these modules, of their pure and refined submodules, of Hill's modules and we also prove an extension of the second Prüfer's theorem.

Structure of flat covers of injective modules

Sh. Payrovi, M. Akhavizadegan (2003)

Colloquium Mathematicae

The aim of this paper is to discuss the flat covers of injective modules over a Noetherian ring. Let R be a commutative Noetherian ring and let E be an injective R-module. We prove that the flat cover of E is isomorphic to ∏ p ∈ A t t R ( E ) T p . As a consequence, we give an answer to Xu’s question [10, 4.4.9]: for a prime ideal p, when does T p appear in the flat cover of E(R/m̲)?

Submodule of free Z-module

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are...

Sur la dualité et la descente d’Iwasawa

David Vauclair (2009)

Annales de l’institut Fourier

Nous développons – en nous appuyant sur l’exemple concret des unités cyclotomiques et du groupe de classes en théorie d’Iwasawa cyclotomique – de nouveaux outils pour une étude générale de la descente et de la codescente, dans l’optique de comparer ces deux points de vue duaux.Si A = ( A n ) est un « système normique » (i.e. une collection de modules galoisiens avec données supplémentaires), attaché à une extension de Lie p -adique fixée d’algèbre d’Iwasawa Λ , nous montrons principalement qu’il existe un...

Sur les Extensions Triviales Commutatives

Farid Kourki (2009)

Annales mathématiques Blaise Pascal

Nous caractérisons les extensions triviales semiGoldie, de cogénération finie, mininjectives et quasi-Frobeniusiens. Comme application, nous montrons que tout anneau noethérien s’injecte dans un anneau quasi-Frobeniusien.

Currently displaying 501 – 520 of 638