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

Luz M. Ruza

Venezuela, Bolivarian Republic of

Universidad de los Andes

Departamento de Matemática, Merida, Venezuela

Jorge Vielma

Venezuela, Bolivarian Republic of

Universidad de los Andes

Departamento de Matem´atica, Merida, Venezuela

Submitted: 2013-09-16

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Accepted: 2013-09-16

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DOI: https://doi.org/10.4995/agt.2011.1696
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Keywords:

Patch topology, Ultrafilter topology, Prime spectrum of a ring

Supporting agencies:

This research was not funded

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
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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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