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All completely regular elements in H y p G ( n )

Ampika Boonmee, Sorasak Leeratanavalee (2013)

Discussiones Mathematicae - General Algebra and Applications

In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties. Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms a monoid. In...

Certain partitions on a set and their applications to different classes of graded algebras

Antonio J. Calderón Martín, Boubacar Dieme (2021)

Communications in Mathematics

Let ( 𝔄 , ϵ u ) and ( 𝔅 , ϵ b ) be two pointed sets. Given a family of three maps ℱ = { f 1 : 𝔄 → 𝔄 ; f 2 : 𝔄 × 𝔄 → 𝔄 ; f 3 : 𝔄 × 𝔄 → 𝔅 } , this family provides an adequate decomposition of 𝔄 ∖ { ϵ u } as the orthogonal disjoint union of well-described ℱ -invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak H * -algebras.

Characterizing binary discriminator algebras

Ivan Chajda (2000)

Mathematica Bohemica

The concept of the (dual) binary discriminator was introduced by R. Halas, I. G. Rosenberg and the author in 1999. We study finite algebras having the (dual) discriminator as a term function. In particular, a simple characterization is obtained for such algebras with a majority term function.

Congruences and ideals in ternary rings

Ivan Chajda, Radomír Halaš, František Machala (1997)

Czechoslovak Mathematical Journal

A ternary ring is an algebraic structure ℛ = ( R ; t , 0 , 1 ) of type ( 3 , 0 , 0 ) satisfying the identities t ( 0 , x , y ) = y = t ( x , 0 , y ) and t ( 1 , x , 0 ) = x = ( x , 1 , 0 ) where, moreover, for any a , b , c ∈ R there exists a unique d ∈ R with t ( a , b , d ) = c . A congruence θ on ℛ is called normal if ℛ / θ is a ternary ring again. We describe basic properties of the lattice of all normal congruences on ℛ and establish connections between ideals (introduced earlier by the third author) and congruence kernels.

Constructions of cell algebras

Alfonz Haviar, Gabriela Monoszová (2005)

Mathematica Bohemica

A construction of cell algebras is introduced and some of their properties are investigated. A particular case of this construction for lattices of nets is considered.

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