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c-ideals in complemented posets

Ivan Chajda, Miroslav Kolařík, Helmut Länger (2024)

Mathematica Bohemica

In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a * -ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions....

Combinatorial trees in Priestley spaces

Richard N. Ball, Aleš Pultr, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

We show that prohibiting a combinatorial tree in the Priestley duals determines an axiomatizable class of distributive lattices. On the other hand, prohibiting n -crowns with n ≥ 3 does not. Given what is known about the diamond, this is another strong indication that this fact characterizes combinatorial trees. We also discuss varieties of 2-Heyting algebras in this context.

Commutative directoids with sectional involutions

Ivan Chajda (2007)

Discussiones Mathematicae - General Algebra and Applications

The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.

Compact pospaces

Venu G. Menon (2003)

Commentationes Mathematicae Universitatis Carolinae

Posets with property DINT which are compact pospaces with respect to the interval topologies are characterized.

Covering energy of posets and its bounds

Vandana P. Bhamre, Madhukar M. Pawar (2023)

Mathematica Bohemica

The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with 2 n elements and a fence with n elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.

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