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Normal autometrized lattice ordered algebras. (English) Zbl 0988.06011
A normal autometrized lattice ordered algebra (N\(A\ell \)-algebra) is an abelian lattice ordered monoid \(A=(A;0,+,\vee ,\wedge)\) with an autometric binary operation \(*\) on \(A\) satisfying certain further conditions. N\(A\ell \)-algebras were introduced by K. L. N. Swamy as a common generalization of abelian lattice ordered groups and Brouwerian lattices. An N\(A\ell \)-algebra \(A\) is called semiregular if \(x\geq 0\) implies \(x*0=x\) for each \(x\in A\). Structure properties of semiregular N\(A\ell \)-algebras were studied by K. L. N. Swamy, N. P. Rao, M. Hansen and the reviewer. In the paper under review, the author proves some of those properties for general N\(A\ell \)-algebras without the assumption of semiregularity.

06F05 Ordered semigroups and monoids
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