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Spectra of autometrized lattice algebras

Jiří Rachůnek (1998)

Mathematica Bohemica

Autometrized algebras are a common generalization e.g. of commutative lattice ordered groups and Brouwerian algebras. In the paper, spectra of normal autometrized lattice ordered algebras (i.e. topologies of sets (and subsets) of their proper prime ideals) are studied. Especially, the representable dually residuated lattice ordered semigroups are examined.

Spectral topologies of dually residuated lattice-ordered monoids

Jan Kühr (2004)

Mathematica Bohemica

Dually residuated lattice-ordered monoids ( D R ℓ -monoids for short) generalize lattice-ordered groups and include for instance also G M V -algebras (pseudo M V -algebras), a non-commutative extension of M V -algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.

Structure of partially ordered cyclic semigroups

Józef Drewniak, Jolanta Sobera (2003)

Czechoslovak Mathematical Journal

This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.

Subtraction semigroups

Bohdan Zelinka (1995)

Mathematica Bohemica

A subtraction semigroup is a semigroup ( A , . , - ) with a further operation " - " added, called subtraction and satisfying certain axioms. The paper concerns a problem by B. M. Schein concerning the structure of multiplication in a subtraction semigroup.

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