Syzygietic properties of a module and torsion freeness of its symmetric powers.

Bonanzinga, Vittoria; Restuccia, Gaetana

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Torsion free exterior powers of a module and their resolutions.

Molica, Giovanni, Restuccia, Gaetana (2002)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Submodule of free Z-module

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

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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...

Purity and direct summands.

Oneto R., Ángel V. (1996)

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Finite and infinite collections of multiplication modules.

Ali, Majid M., Smith, David J. (2001)

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Lomp, Christian (2006)

Beiträge zur Algebra und Geometrie

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Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

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Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that $E x t_{R} (G, G) = 0$ . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which...