On a common abstraction of Boolean rings and lattice ordered groups I

@article{Rao1972OnAC,
  title={On a common abstraction of Boolean rings and lattice ordered groups I},
  author={V. V. Rama Rao},
  journal={Monatshefte f{\"u}r Mathematik},
  year={1972},
  volume={73},
  pages={411-421}
}
  • V. Rao
  • Published 1 October 1969
  • Mathematics
  • Monatshefte für Mathematik
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 special cases? The solution actually turns out to be the direct product of a Boolean ring and a lattice ordered group. Birkhoff's problem has also been solved by Swamy, Wyler, and Nakano by presenting respectively i) Dually Residuated Lattice Ordered Semigroups (D.R.1. semigroups) [2, 3, 4, 5], ii… 
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6 Citations
Background Citations
3
Results Citations
1

6 Citations

A common abstraction of boolean rings and lattice ordered groups
Lattice ordered partial semigroups are introduced as a common abstraction of Boolean rings and lattice ordered groups. Boolean rings and lattice ordered groups are characterized as lattice ordered…
Minimal clans: A class of ordered partial semigroups including boolean rings and lattice-ordered groups
The present paper contains a rather comprehensive investigation of the properties of minimal clans — a new class of ordered partial semigroups which includes Boolean rings and lattice-ordered groups…
Ordered Algebras and Logic
Ordered algebras such as Boolean algebras, Heyting algebras, lattice-ordered groups, and MV-algebras have long played a decisive role in logic, although perhaps only in recent years has the…
SMARANDACHE – BOOLEAN – NEAR – RINGS AND ALGORITHMS WITH EXAMPLES
In this paper we introduced Smarandache-2-algebraic structure of Boolean-near-ring namely Smarandache-Boolean-nearring. A Smarandache-2-algebraic structure on a set N means a weak algebraic structure…
On Birkhoff’s Common Abstraction Problem
TLDR
A Holland-type representation theorem is proved for a variety of FL-algebras containing a common generalization of B and A and their join in the lattice of subvarieties of F, which is optimal under several respects.
Ideals in autometrized algebras
  • K. SwamyN. Rao
  • Mathematics
    Journal of the Australian Mathematical Society
  • 1977
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…

References

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Transitivities of Betweenness
Introduction. The examination of the foundations of geometry which interested many prominent mathematicians about the turn of the century brought to light the importance of the fundamental notion of…
On a Common Abstraction of Booleanrings and Lattice Ordered groups 1
  • Monat. Fur. Math
  • 1969
Dually Residuated Lattice Ordered Semigroups, III
Dually Residuated Lattice Ordered Semigroups, II
Dually residuated lattice ordered semigroups
Rings and partly ordered systems
Review: G. Birkhoff, Lattice theory
' On a Common Abstraction of Booleanrings and Lattice Ordered groups 1 ' , Monat
  • Fur . Math .
  • 1969
Birkhoff , Lattice Theory ( Amer . Math . Soc . Col . Pub XXV , 1948 ) . [ 2 ] K . L . N . Swamy , ' Dually Residuated Lattice Ordered Semigroups '
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