On some varieties of weakly associative lattice groups
On spectral continuity of positive elements
Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the...
On strictly positive lattice ordered semigroups
On subdirectly irreducible lattice-ordered semigroups .
On subdirectly irreducible ordered semigroups.
On summability in convergence -groups
On the additive semigroup of ordered semirings.
On the additive semigroup structure of semirings.
On the additive structure of a class of ordered semirings.
On the affine completeness of lattice ordered groups
In the paper it is proved that a nontrivial direct product of lattice ordered groups is never affine complete.
On the algebraic properties of convex bodies and some applications.
On the class of QS-algebras.
On the classes of orderable semigroups in varieties.
On the completion of cyclically ordered groups
On the congruence lattice of an abelian lattice ordered group
In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
On the construction and the realization of wild monoids
We develop elementary methods of computing the monoid for a directly-finite regular ring . We construct a class of directly finite non-cancellative refinement monoids and realize them by regular algebras over an arbitrary field.
On the construction of some semigroups
On the decomposition of prime ideals of ordered semigroups into their N-classes.
On the degrees of permutability of subregular varieties
On the distributive radical of an Archimedean lattice-ordered group
Let be an Archimedean -group. We denote by and the divisible hull of and the distributive radical of , respectively. In the present note we prove the relation . As an application, we show that if is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.