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BLAST 2008
August 6-10, 2008
University of Denver
Denver, CO, USA

Organizers
Rick Ball, Natasha Dobrinen (co-chair), Nikolaos Galatos (co-chair)

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Alexandroff topologies and semirings
by
Jorge Vielma
Universidad de los Andes
Coauthors: A Peņa and L Ruza

In this work by a semiring R we understand a commutative semiring with identity. Spec(R) denotes the set of all prime ideals of R, equiped with the Zariski topology tz

We prove that (Spec(R), tz) is Alexandroff if and only if R is a Gilmer semiring.

References

[1] Alarcon F and Anderson D, Commutative semirings and their lattices of ideals, Houston Journal of Mathematics. 20 (4) (1994), 571-590.

[2] Golan J. S, Semirings and their applications, Kluwer Academic Publishers, Dordrecht (1999).

[3] Uzcategui, C. and Vielma, J., Alexandroff Topologies viewed as closed subsets of the Cantor cube, Divulgaciones Matematicas. 13 (1)(2005), 45-53

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Date received: May 28, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxi-17.