• Title, Summary, Keyword: topological algebra

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FUZZY IMPLICATIVE ALGEBRAS

  • Jun, Young-Bae;Kim, Hee-Sik
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.109-117
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    • 1999
  • We introduce the notion of a fuzzy topological implicative algebras and apply some of Foster's results [2] to homomorphic images and inverse images of fuzzy topological implicative algebras.

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UNIFORM TOPOLOGY ON DIFFERENCE ALGEBRAS

  • SAEID, ARSHAM BORUMAND
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.2
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    • pp.379-386
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    • 2005
  • In this paper, we consider a collection of ideals of a difference algebra X. We use the concept of congruence relation with respect to ideals to construct a uniformity that induces a topology on X which makes this to a topological difference algebras. We study the properties of this topology regarding different ideals.

SOME CURIOSITIES OF THE ALGEBRA OF BOUNDED DIRICHLET SERIES

  • Mortini, Raymond;Sasane, Amol
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.153-161
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    • 2016
  • It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.

A Completion of Semi-simple MV-algebra

  • 박평우
    • 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.

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REGULAR GLOSED BOOLEAN ALGBRA IN THE SPACE WITH EXTENSION TOPOLOGY

  • Cao, Shangmin
    • The Pure and Applied Mathematics
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    • v.7 no.2
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    • pp.71-78
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    • 2000
  • Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

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PRIME FILTERS OF COMMUTATIVE BE-ALGEBRAS

  • RAO, M. SAMBASIVA
    • Journal of applied mathematics & informatics
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    • v.33 no.5_6
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    • pp.579-591
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    • 2015
  • Properties of prime filters are studied in BE-algebras as well as in commutative BE-algebras. An equivalent condition is derived for a BE-algebra to become a totally ordered set. A condition L is introduced in a commutative BE-algebra in ordered to study some more properties of prime filters in commutative BE-algebras. A set of equivalent conditions is derived for a commutative BE-algebra to become a chain. Some topological properties of the space of all prime filters of BE-algebras are studied.

SPECTRAL DUALITIES OF MV-ALGEBRAS

  • Choe, Tae-Ho;Kim, Eun-Sup;Park, Young-Soo
    • 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.

UNIVERSAL HYPERDYNAMICAL SYSTEMS

  • Nezhad, A. Dehghan;Davvaz, B.
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.513-526
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    • 2010
  • In this paper, the theory of n-ary hypergroups and some applications of hyperalgebras (Fredholm-Voltra integral, copula) are studied. We define some new concepts of topological hyperdynamical systems, universal hyperdynamical systems and immersed universal hyperalgebra. Also, we present some results in this respect.