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Goldie extending elements in modular lattices

Shriram K. Nimbhorkar, Rupal C. Shroff (2017)

Mathematica Bohemica

The concept of a Goldie extending module is generalized to a Goldie extending element in a lattice. An element a of a lattice L with 0 is said to be a Goldie extending element if and only if for every b ≤ a there exists a direct summand c of a such that b ∧ c is essential in both b and c . Some properties of such elements are obtained in the context of modular lattices. We give a necessary condition for the direct sum of Goldie extending elements to be Goldie extending. Some characterizations of a decomposition...

Gosset polytopes in integral octonions

Woo-Nyoung Chang, Jae-Hyouk Lee, Sung Hwan Lee, Young Jun Lee (2014)

Czechoslovak Mathematical Journal

We study the integral quaternions and the integral octonions along the combinatorics of the 24 -cell, a uniform polytope with the symmetry D 4 , and the Gosset polytope 4 21 with the symmetry E 8 . We identify the set of the unit integral octonions or quaternions as a Gosset polytope 4 21 or a 24 -cell and describe the subsets of integral numbers having small length as certain combinations of unit integral numbers according to the E 8 or D 4 actions on the 4 21 or the 24 -cell, respectively. Moreover, we show that each...

Graph automorphisms and cells of lattices

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

In this paper we apply the notion of cell of a lattice for dealing with graph automorphisms of lattices (in connection with a problem proposed by G. Birkhoff).

Graph automorphisms of multilattices

Mária Csontóová (2003)

Mathematica Bohemica

In the present paper we generalize a result of a theorem of J. Jakubík concerning graph automorphisms of lattices to the case of multilattices of locally finite length.

Ideals in distributive posets

Cyndyma Batueva, Marina Semenova (2011)

Open Mathematics

We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.

Implications partielles dans un contexte

Michael Luxenburger (1991)

Mathématiques et Sciences Humaines

Nous présentons une extension de la théorie des implications entre attributs binaires aux implications partielles. A partir de données expérimentales on s'intéresse non seulement aux implications (globales), mais aussi aux «implications avec quelques contre exemples». Les implications partielles offrent une possibilité d'extraire des informations supplémentaires. Elles permettent de «modéliser» la fréquence relative d'une implication, non-valide pour toutes les données, et donnent par conséquent...

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