Baer sums and fibered aspects of Mal'cev operations
Balanced congruences
Let V be a variety with two distinct nullary operations 0 and 1. An algebra 𝔄 ∈ V is called balanced if for each Φ,Ψ ∈ Con(𝔄), we have [0]Φ = [0]Ψ if and only if [1]Φ = [1]Ψ. The variety V is called balanced if every 𝔄 ∈ V is balanced. In this paper, balanced varieties are characterized by a Mal'cev condition (Theorem 3). Furthermore, some special results are given for varieties of bounded lattices.
Balanced d-lattices are complemented
We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
Bases in incidence structures defined on projective spaces
Betweenness spaces and tree algebras
Bijective reflexions and coreflexions of commutative unars
Binary hyperidentities.
Binary relations on the monoid of V-proper hypersubstitutions
In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.
Biregular and uniform identities of algebras
Birkhoff variety theorem for finite algebras
Boolean matrices ... neither Boolean nor matrices
Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
Boolean powers as algebras of continuous functions [Book]
Boolean semirings
Bounded countable atomic compactness of ordered groups