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We develop problems of monotonic valuations of triads. A theorem on monotonic valuations of triads of the type $π σ$ is presented. We study, using the notion of the monotonic valuation, representations of ideals by monotone and subadditive mappings. We prove, for example, that there exists, for each ideal $J$ of the type $π$ on a set $A$ , a monotone and subadditive set-mapping $h$ on $P (A)$ with values in non-negative rational numbers such that $J = h^{- 1}^{''} {r \in Q; r \geq 0 & r ≐ 0}$ . Some analogical results are proved for ideals of the types $σ, σ π$ and...

M-Solid Subvarieties of some Varieties of Commutative Semigroups

Koppitz, J. (1997)

Serdica Mathematical Journal

∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent.

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Modularity and distributivity of tolerance lattices of commutative separative semigroups

Modularity and distributivity of tolerance lattices of commutative inverse semigroups

Monoides et semi-anneaux complets.

Monoides et semi-anneaux continus.

Monotonic valuations of π σ -triads and evaluations of ideals

M-Solid Subvarieties of some Varieties of Commutative Semigroups

Currently displaying 1 – 6 of 6

Monotonic valuations of $π σ$ -triads and evaluations of ideals