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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.

Split structures.

Rosebrugh, Robert, Wood, R.J. (2004)

Theory and Applications of Categories [electronic only]

State-homomorphisms on M V -algebras

Ján Jakubík (2001)

Czechoslovak Mathematical Journal

Riečan [12] and Chovanec [1] investigated states in M V -algebras. Earlier, Riečan [11] had dealt with analogous ideas in D -posets. In the monograph of Riečan and Neubrunn [13] (Chapter 9) the notion of state is applied in the theory of probability on M V -algebras. We remark that a different definition of a state in an M V -algebra has been applied by Mundici [9], [10] (namely, the condition (iii) from Definition 1.1 above was not included in his definition of a state; in other words, only finite additivity...

States on basic algebras

Ivan Chajda, Helmut Länger (2017)

Mathematica Bohemica

States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain...

Stone Lattices

Adam Grabowski (2015)

Formalized Mathematics

The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the other which...

Strongly fixed ideals in C ( L ) and compact frames

A. A. Estaji, A. Karimi Feizabadi, M. Abedi (2015)

Archivum Mathematicum

Let C ( L ) be the ring of real-valued continuous functions on a frame L . In this paper, strongly fixed ideals and characterization of maximal ideals of C ( L ) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C ( L ) , is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than...

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