Ideals in autometrized algebras

  title={Ideals in autometrized algebras},
  author={K. L. N. Swamy and N. Prabhakara Rao},
  journal={Journal of the Australian Mathematical Society},
  pages={362 - 374}
  • K. Swamy, N. Rao
  • Published 1 November 1977
  • Mathematics
  • Journal of the Australian Mathematical Society
Abstract A notion of a normal autometrized algebra is introduced which generalises the concepts of Boolean geometry. Brouwerian geometry, autometrized lattice ordered groups, semi-Brouwerian geometry, etc. The notions of ideals and congruence relations are introduced in normal autometrized algebras and a one to one correspondence between ideals and congruence relations is established. Some other common properties of the above geometries are also obtained for normal autometrized algebras. 
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A duality between algebras of basic logic and bounded representable $DRl$-monoids
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Direct decompositions of dually residuated lattice-ordered monoids
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On lattice-ordered monoids
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Annihilators in Normal Autometrized Algebras
AbstractThe concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra
DRl-semigroups and MV-algebras


Autometrized Boolean Algebras II
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  • Mathematics
    Canadian Journal of Mathematics
  • 1951
The writer [1] has previously examined the fundamental concepts of distance geometry in a Boolean algebra, B, with distance defined by . Any technical terms from distance geometry which are not
Semi-Brouwerian algebras
  • P. V. R. Murty
  • Mathematics
    Journal of the Australian Mathematical Society
  • 1974
Ever since David Ellis has shown that a Boolean algebra has a natural structure of an autometrized space, the interest in such spaces has led several authors to study various autometrized algebras
On a common abstraction of Boolean rings and lattice ordered groups I
  • V. Rao
  • Mathematics
    Journal of the Australian Mathematical Society
  • 1972
In an earlier paper, the author has obtained a solution [8] to Birkhoff's problem No. 105 [1]: Is there a common abstraction which includes Boolean algebras (Rings) and lattice ordered groups as
Boolean Geometry 1
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Dually Residuated Lattice
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