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ON MULTIPLIERS ON BOOLEAN ALGEBRAS

  • Kim, Kyung Ho (Department of Mathematics, Korea National University of Transportation)
  • 투고 : 2016.07.29
  • 심사 : 2016.10.13
  • 발행 : 2016.11.15

초록

In this paper, we introduced the notion of multiplier of Boolean algebras and discuss related properties between multipliers and special mappings, like dual closures, homomorphisms on B. We introduce the notions of xed set $Fix_f(X)$ and normal ideal and obtain interconnection between multipliers and $Fix_f(B)$. Also, we introduce the special multiplier ${\alpha}_p$a nd study some properties. Finally, we show that if B is a Boolean algebra, then the set of all multipliers of B is also a Boolean algebra.

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참고문헌

  1. R. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, United States, 1974.
  2. G. Birkhoof, Lattice Theory, American Mathematical Society Colloquium, 1940.
  3. R. Larsen, An Introduction to the Theory of Multipliers, Berlin: Springer-Verlag, 1971.
  4. E. Mendelson, Schaum's outline of theory and problems of Boolean algebra and Switsching circuits, McGraw-Hill Inc, U.S.A.
  5. Sureeporn Harmaitree and Utsanee Leerawat, On f-derivations in lattices, Far East Journal of Mathematical Sciences, 51 (1) (2011), 27-40.