A Completion of Semi-simple MV-algebra

  • 박평우 (성균관대학교 수학교육과)
  • 발행 : 2000.06.01

초록

The notion of MV-algebra was introduced by C.C. Chang in 1958 to provide an algebraic proof of the completeness of Lukasiewicz axioms for infinite valued logic. These algebras appear in the literature under different names: Bricks, Wajsberg algebra, CN-algebra, bounded commutative BCK-algebras, etc. The purpose of this paper is to give a topological lattice completion of semisimple MV-algebras. To this end, we characterize the complete atomic center MV-algebras and semisimple algebras as subalgebras of a cube. Then we define the $\delta$-completion of semisimple MV-algebra and construct the $\delta$-completion. We also study some important properties and extension properties of $\delta$-completion.

키워드

참고문헌

  1. Can. J. Math. XXXVII v.6 Semi-simple algebras of infinite valued logic and bold fuzzy set theory Belluce, L.P.
  2. Algebras Universalis v.29 Semi-simple and complete MV-algebras Belluce, L.P.
  3. Trans. AMS v.88 Algebraic analysis of many-valued logics Chang, C.C.
  4. Trans. AMS v.93 A new proof of completeness of Lukasiewicz axioms Chang, C.C.
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  6. Math. Japonica v.4 MV-algebras, Ideals and Semisimplictiy Hoo, C.S.
  7. Boll. U.M.I. v.4 On certain algebra related to many-valued logics (Italian) Mangani, P.