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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 $ℱ = {f_{1} : 𝔄 \to 𝔄; f_{2} : 𝔄 \times 𝔄 \to 𝔄; f_{3} : 𝔄 \times 𝔄 \to 𝔅}$ , 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.

Chains of Decompositions and $n$ -Ary Relations

Ivan Žembery (1973)

Matematický časopis

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.

Classes of graphs definable by graph algebra identities or quasi-identities

Reinhard Pöschel, Walter Wessel (1987)

Commentationes Mathematicae Universitatis Carolinae

Clone compatible identities and clone extensions of algebras

Jerzy Płonka (1997)

Mathematica Slovaca

Clones in topology and algebra.

Sichler, J., Trnková, V. (1997)

Acta Mathematica Universitatis Comenianae. New Series

Coherence and weak coherence in the square of algebras

Jaromír Duda (1992)

Czechoslovak Mathematical Journal

Compact elements of the lattice of congruences in an algebra

Jitka Ševečková (1977)

Časopis pro pěstování matematiky

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 $a$ , $b$ , $c \in R$ there exists a unique $d \in R$ 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.

Convex sets in algebras

Radim Bělohlávek (2002)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Currently displaying 1 – 11 of 11

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