The equality of the Patch topology and the Ultrafilter topology: A shortcut

Luz M. Ruza, Jorge Vielma

Abstract

In this work R denotes a commutative ring with non-zero identity andwe prove that the patch topology and the ultrafilter topology definedon the prime spectrum of R are equal, in a different way as the givenby Marco Fontana and K. Alan Loper

Keywords

Patch topology; Ultrafilter topology; Prime spectrum of a ring

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References

M. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1969.

M. Fontana and K. A. Loper, The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring, Comm. Algebra 36 (2008), 2917–2922. http://dx.doi.org/10.1080/00927870802110326

M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43–60. http://dx.doi.org/10.1090/S0002-9947-1969-0251026-X

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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt