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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 → 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.

Characterizing matrices with 𝐗 -simple image eigenspace in max-min semiring

Ján Plavka, Sergeĭ Sergeev (2016)

Kybernetika

A matrix A is said to have 𝐗 -simple image eigenspace if any eigenvector x belonging to the interval 𝐗 = { x : x ̲ ≤ x ≤ x ¯ } is the unique solution of the system A ⊗ y = x in 𝐗 . The main result of this paper is a combinatorial characterization of such matrices in the linear algebra over max-min (fuzzy) semiring. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability) that...

Characterizing pure, cryptic and Clifford inverse semigroups

Mario Petrich (2014)

Czechoslovak Mathematical Journal

An inverse semigroup S is pure if e = e 2 , a ∈ S , e < a implies a 2 = a ; it is cryptic if Green’s relation ℋ on S is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize groups and...

Characterizing tolerance trivial finite algebras

Ivan Chajda (1994)

Archivum Mathematicum

An algebra A is tolerance trivial if A ̰ = A where A ̰ is the lattice of all tolerances on A . If A contains a Mal’cev function compatible with each T A ̰ , then A is tolerance trivial. We investigate finite algebras satisfying also the converse statement.

Class preserving mappings of equivalence systems

Ivan Chajda (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

By an equivalence system is meant a couple 𝒜 = ( A , θ ) where A is a non-void set and θ is an equivalence on A . A mapping h of an equivalence system 𝒜 into ℬ is called a class preserving mapping if h ( [ a ] θ ) = [ h ( a ) ] θ ' for each a ∈ A . We will characterize class preserving mappings by means of permutability of θ with the equivalence Φ h induced by h .

Currently displaying 241 – 260 of 2109