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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...

Sturdy frames of type (2,2) algebras and their applications to semirings

X. Z. Zhao, Y. Q. Guo, K. P. Shum (2003)

Fundamenta Mathematicae

We introduce sturdy frames of type (2,2) algebras, which are a common generalization of sturdy semilattices of semigroups and of distributive lattices of rings in the theory of semirings. By using sturdy frames, we are able to characterize some semirings. In particular, some results on semirings recently obtained by Bandelt, Petrich and Ghosh can be extended and generalized.

Subdirectly irreducible MV-algebras

Hernando Gaitan (2003)

Czechoslovak Mathematical Journal

In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety.

Subdirectly irreducible sectionally pseudocomplemented semilattices

Radomír Halaš, Jan Kühr (2007)

Czechoslovak Mathematical Journal

Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented...

Sublocale sets and sublocale lattices

Jorge Picado, Aleš Pultr (2006)

Archivum Mathematicum

We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.

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