# 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} }

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…

## 6 Citations

A common abstraction of boolean rings and lattice ordered groups

- Mathematics
- 2019

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

- Mathematics
- 1988

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

- Mathematics
- 2010

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

- Mathematics
- 2016

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

- MathematicsStud Logica
- 2012

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

- MathematicsJournal 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…

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