• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.481-489
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• 2005

We first show that any complete MV-algebra whose Boolean subalgebra of idempotent elements is atomic, called a complete MV-algebra with atomic center, is isomorphic to a product of unit interval MV-algebra 1's and finite linearly ordered MV-algebras of A(m)-type $(m{\in}{\mathbb{Z}}^+)$. Secondly, for a semi-simple MV-algebra A, we introduce a completion ${\delta}(A)$ of A which is a complete, MV-algebra with atomic center. Under their intrinsic topologies $(see\;{\S}3)$ A is densely embedded into ${\delta}(A)$. Moreover, ${\delta}(A)$ has the extension universal property so that complete MV-algebras with atomic centers are epireflective in semi-simple MV-algebras

• 한국수학사학회지
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• 제13권1호
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• pp.125-136
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• 2000

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.

• 대한수학회지
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• 제42권6호
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• pp.1111-1120
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• 2005

Hong and Nel in [8] obtained a number of spectral dualities between a cartesian closed topological category X and a category of algebras of suitable type in X in accordance with the original formalism of Porst and Wischnewsky[12]. In this paper, there arises a dual adjointness S $\vdash$ C between the category X = Lim of limit spaces and that A of MV-algebras in X. We firstly show that the spectral duality: $S(A)^{op}{\simeq}C(X^{op})$ holds for the dualizing object K = I = [0,1] or K = 2 = {0, 1}. Secondly, we study a duality between the category of Tychonoff spaces and the category of semi-simple MV-algebras. Furthermore, it is shown that for any $X\;\in\;Lim\;(X\;{\neq}\;{\emptyset})\;C(X,\;I)$ is densely embedded into a cube $I^/H/$, where H is a set.