Horizontal sums of basic algebras
The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
How can representation theories of inverse semigroups and lattices be united?
How many four-generated simple lattices
How to draw tolerance lattices of finite chains
Hu's Primal Algebra Theorem revisited
It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.
Hyper BCI-algebras
We introduce the concept of a hyper BCI-algebra which is a generalization of a BCI-algebra, and investigate some related properties. Moreover we introduce a hyper BCI-ideal, weak hyper BCI-ideal, strong hyper BCI-ideal and reflexive hyper BCI-ideal in hyper BCI-algebras, and give some relations among these hyper BCI-ideals. Finally we discuss the relations between hyper BCI-algebras and hyper groups, and between hyper BCI-algebras and hyper -groups.
Hyperarchimedische Teilbarkeitshalbgruppen
Hypergroupes et groupes ordonnés
Hyperstructures Associated with Ordered sets
Hypersubstitutions in orthomodular lattices
It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.
Ideal extensions of ordered sets.
Ideal independence, free sequences, and the ultrafilter number
We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in Baumgartner J.E., Komjáth P., Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125–133, Koszmider P., Forcing minimal extensions of Boolean algebras, Trans. Amer. Math. Soc. 351 (1999), no. 8, 3073–3117, and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, such that , answering questions raised by Monk...
Ideal nil-extensions of semigroups with semimodular congruence lattices.
Ideal systems and lattice theory.
Ideal systems of intersection and product type
Ideal theory in commutative semigroups.
Ideale in Rechtsverbandshalbgruppen.
Ideals and Green's relations in ordered semigroups.
Ideals, congruences and annihilators on nearlattices
By a nearlattice is meant a join-semilattice having the property that every principal filter is a lattice with respect to the semilattice order. We introduce the concept of (relative) annihilator of a nearlattice and characterize some properties like distributivity, modularity or -distributivity of nearlattices by means of certain properties of annihilators.
Ideals in distributive posets
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.