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Radicals and complete distributivity in relatively normal lattices

Jiří Rachůnek (2003)

Mathematica Bohemica

Lattices in the class $ℐℛ𝒩$ of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in $ℐℛ𝒩$ the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in $ℐℛ𝒩$ with the sublattice of compact elements satisfying the conditional join-infinite distributive law they are compared with two other kinds of radicals. Connections between complete distributivity of algebraic...

Regularity in p-algebras and p-semilattices

J. Varlet (1982)

Banach Center Publications

Relatively pseudocomplemented directoids

Ivan Chajda (2009)

Commentationes Mathematicae Universitatis Carolinae

The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called $p$ -ideals.

Relatively pseudocomplemented posets

Ivan Chajda, Helmut Länger (2018)

Mathematica Bohemica

We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relatively pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending chain...

Remarks on $Q$ -independence of Stone algebras

Anna Chwastyk, Kazimierz Głazek (2006)

Mathematica Slovaca

Representation of certain classes of distributive lattices by sections of sheaves.

Swamy, U.Maddana, Manikyamba, P. (1980)

International Journal of Mathematics and Mathematical Sciences

Retracts and Q-independence

Anna Chwastyk (2007)

Discussiones Mathematicae - General Algebra and Applications

A non-empty set X of a carrier A of an algebra A is called Q-independent if the equality of two term functions f and g of the algebra A on any finite system of elements a₁,a₂,...,aₙ of X implies f(p(a₁),p(a₂),...,p(aₙ)) = g(p(a₁),p(a₂),...,p(aₙ)) for any mapping p ∈ Q. An algebra B is a retract of A if B is the image of a retraction (i.e. of an idempotent endomorphism of B). We investigate Q-independent subsets of algebras which have a retraction in their set of term functions.