Kyungpook Mathematical Journal

  • 제48권3호
  • /
  • Pages.487-493
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  • 2008
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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MV -Algebras of Continuous Functions and l-Monoids

  • Choe, Tae-Ho (Department of Math. Stat. McMaster University Hamilton) ;
  • Kim, Eun-Sup (Department of Math.College of Natural Sciences Kyungpook National University) ;
  • Kim, Myeong-Og (Department of Math.College of Natural Sciences Kyungpook National University) ;
  • Park, Young-Soo (Department of Math.College of Natural Sciences Kyungpook National University)
  • 투고 : 2008.02.28
  • 발행 : 2008.09.30
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초록

A. Di Nola & S.Sessa [8] showed that two compact spaces X and Y are homeomorphic iff the MV -algebras C(X, I) and C(Y, I) of continuous functions defined on X and Y respectively are isomorphic. And they proved that A is a semisimple MV -algebra iff A is a subalgebra of C(X) for some compact Hausdorff space X. In this paper, firstly by use of functorial argument, we show these characterization theorems. Furthermore we obtain some other functorial results between topological spaces and MV -algebras. Secondly as a classical problem, we find a necessary and sufficient condition on a given residuated l-monoid that it is segmenently embedded into an l-group with order unit.

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참고문헌

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