• Honam Mathematical Journal
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• v.38 no.3
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• pp.643-659
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• 2016

In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.253-265
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• 2018

In this paper, we introduce the concept of Fibonacci sequences on MV-algebras and study them accurately. Also, by introducing the concepts of periodic sequences and power-associative MV-algebras, other properties are also obtained. The relation between MV-algebras and Fibonacci sequences is investigated.

• Journal for History of Mathematics
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• v.13 no.1
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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.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.37-44
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• 2002

In this paper, we obtain an algebraic structure which is equivalent to an MV-algebra. Moreover, we show that $t$-norm and $t$-conorm can be obtained from MV-algebras.

• Kyungpook Mathematical Journal
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• v.45 no.4
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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

• Journal for History of Mathematics
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• v.20 no.1
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• pp.73-82
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• 2007

This paper delineates some history and developments of Wajsberg hoops, MV-algebras and commutative BCK-algebras. It also discuss some relations on them. Finally, it shows that every Wajsberg hoop is a commutative BCK-algebra.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.649-652
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• 2001

In this paper, we introduce neighborhood systems in an L-fuzzy topology using complete MV-algebras. We investigate the relationship between L-fuzzy topologies and the neighborhood systems. We study the properties of neighborhood system.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.487-493
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• 2008

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.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.282-287
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• 2002

In this paper, we introduce the degrees of fuzzy net-convergences in L-fuzzy topologies using complete MV-algebras. We investigate the relationships among the degrees of fuzzy convergent, fuzzy cluster and fuzzy adherent points. We study the properties of net-convergences.