Ideals in autometrized algebras
@article{Swamy1977IdealsIA,
title={Ideals in autometrized algebras},
author={K. L. N. Swamy and N. Prabhakara Rao},
journal={Journal of the Australian Mathematical Society},
year={1977},
volume={24},
pages={362 - 374}
}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.
8 Citations
Spectra of autometrized lattice algebras
- Mathematics
- 1998
Autometrized algebras are a common generalization e.g. of commutative lattice ordered groups and Brouwerian algebras. In the paper, spectra of normal autometrized lattice ordered algebras (i.e.…
A DUALITY BETWEEN ALGEBRAS OF BASIC LOGIC AND BOUNDED REPRESENTABLE DRl-MONOIDS
- Mathematics
- 2001
BL-algebras, introduced by P. Hajek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that BL-algebras are the duals of bounded representable DRl-monoids. This duality…
A duality between algebras of basic logic and bounded representable $DRl$-monoids
- Mathematics
- 2001
$BL$-algebras, introduced by P. Hajek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that $BL$-algebras are the duals of bounded representable $DRl$-monoids. This…
Direct decompositions of dually residuated lattice-ordered monoids
- Mathematics
- 2004
The class of dually residuated lattice ordered monoids (DR`-monoids) contains, in an appropriate signature, all `-groups, Brouwerian algebras, MV and GMV -algebras, BLand pseudo BL-algebras, etc. In…
On lattice-ordered monoids
- Mathematics
- 2003
In the paper lattice-ordered monoids and specially normal latticeordered monoids which are a generalization of dually residuated latticeordered semigroups are investigated. Normal lattice-ordered…
Annihilators in Normal Autometrized Algebras
- Mathematics
- 2001
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 …
References
SHOWING 1-10 OF 16 REFERENCES
Autometrized Boolean Algebras II
- MathematicsCanadian 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
- MathematicsJournal 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
- MathematicsJournal 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
- Lattice Theory, (Amer. Math. Soc. Col. Publications, 3rd Edition, 2nd Printing,
- 1973
Dually Residuated Lattice
- Ordered Semigroups', Math. Annalen
- 1965