A Note on Boolean Like Algebras

 
 
 
  • Abstract
  • Keywords
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  • Abstract


    In this paper we develop on abstract system: viz Boolean-like algebra and prove that every Boolean  algebra is a Boolean-like algebra.  A necessary and sufficient condition for a Boolean-like algebra to be a Boolean algebra has been obtained.  As in the case of Boolean ring  and Boolean algebra, it is established that under suitable binary operations the Boolean-like ring and Boolean-like algebra are equivalent abstract structures.

     


  • Keywords


    Boolean algebra; Boolean like algebra; Boolean like ring; Boolean ring;

  • References


      [1] Bhattacharya P.B., (1995) etc Basic Abstract Algebra, 2nd edition, Cambridge University Press

      [2] Foster, A.L. (1951), pk –rings and ring-logics, Ann.sci.Norm Pisa 5,279-300.

      [3] George F. Simmons (1963), Introduction to Topology and Modern Analysis, McGraw – Hill Book, Company, Inc

      [4] Jachim Lambek (1986) , Lectures on Rings and Modules, 3rd edition Chelsea pub. Company, New York, N.Y.

      [5] Swaminathan, V (1982 ), Boolean-like rings Ph.D thesis, A.U.

      [6] Thomas W. Hungerford(1974), Algebra, Holt, Rinehart and Winston, INC., New York


 

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Article ID: 26660
 
DOI: 10.14419/ijet.v7i4.10.26660




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