Article
Keywords:
$\mathit{DR}\ell $-monoid; $\mathit{GPMV}$-algebra; Archimedean property
Summary:
In this note we describe the structure of dually residuated $\ell $-monoids ($\mathit{DR}\ell $-monoids) that have no non-trivial convex subalgebras.
References:
[1] Anderson M., Feil T.: Lattice-Ordered Groups (An Introduction). :
D. Reidel, Dordrecht. 1988.
MR 0937703
[3] Georgescu G., Leuştean L., Preoteasa V.:
Pseudo-hoops. J. Mult.-Val. Log. Soft Comput. 11 (2005), 153–184.
MR 2162590 |
Zbl 1078.06007
[4] Glass A. M. W.: Partially Ordered Groups. :
World Scientific, Singapore. 1999.
MR 1791008
[5] Jipsen P., Tsinakis C.:
A survey of residuated lattices. In: Ordered Algebraic Structures (Martinez, J., ed.), Kluwer Acad. Publ., Dordrecht, 2002, pp. 19–56.
MR 2083033 |
Zbl 1070.06005
[6] Kovář T.: A General Theory of Dually Residuated Lattice Ordered Monoids. : Ph.D. thesis, Palacký University, Olomouc. 1996.
[7] Kühr J.:
Ideals of noncommutative $DR\ell $-monoids. Czechoslovak Math. J. 55 (2005), 97–111.
MR 2121658
[8] Kühr J.:
On a generalization of pseudo MV-algebras. J. Mult.-Val. Log. Soft Comput. (to appear).
MR 2288689
[9] Kühr J.:
Generalizations of pseudo MV-algebras and generalized pseudo effect algebras. Submitted.
Zbl 1174.06330
[10] Swamy K. L. N.:
Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105–114.
MR 0183797 |
Zbl 0138.02104