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arXiv · 1511.09169

A generalization of quantales with applications to modules and rings

Mauricio Medina Bárcenas·Angel Zaldívar·Martha Lizbeth Shaid Sandoval Miranda
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Abstract

We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R$-modules. In particular, we give the module counterpart of the well known result that in a commutative ring the set of semiprime ideals, that is, the set of radical ideals is a frame.

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Mauricio Medina Bárcenas, Angel Zaldívar, Martha Lizbeth Shaid Sandoval Miranda. 2015-11-30. A generalization of quantales with applications to modules and rings. https://arxiv.org/abs/1511.09169

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