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Two remarks on dually residuated lattice ordered semigroups. (English) Zbl 0943.06007
Dually residuated lattice-ordered semigroups (DRl-semigroups) were introduced by K. L. N. Swamy [Math. Ann. 159, 105-114 (1965; Zbl 0135.04203)] as a common generalization of abelian lattice-ordered groups and Brouwerian algebras. In this note a somewhat simpler system of axioms for DRl-semigroups is found. It is also shown that certain autometrics in a DRl-semigroup defined by K. L. N. Swamy are identical.

MSC:
06F05 Ordered semigroups and monoids
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References:
[1] KOVÁŘ T.: Any \(DR\ell\)-semigroup is the direct product of a commutative \(\ell\)-group and a \(DR\ell\)-semigroup with the least element. Discuss. Math. Algebra Stochastic Methods 16 (1996), 99-105. · Zbl 0869.06011
[2] SWAMY K. L. N.: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105-114. · Zbl 0138.02104 · doi:10.1007/BF01364335 · eudml:161279
[3] SWAMY K. L. N.: Dually residuated lattice ordered semigroups II. Math. Ann. 160 (1965), 64-71. · Zbl 0138.02104 · doi:10.1007/BF01364335 · eudml:161279
[4] SWAMY K. L. N.: Dually residuated lattice ordered semigroups III. Math. Ann. 167 (1966), 71-74. · Zbl 0158.02601 · doi:10.1007/BF01361218 · eudml:161473
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