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Cancellative relations and matrices

Ladislav Bican, Aleš Drápal, Tomáš Kepka (1987)

Acta Universitatis Carolinae. Mathematica et Physica

Caratterizzazione di una classe di anelli generalizzati

Domenico Boccioni (1965)

Rendiconti del Seminario Matematico della Università di Padova

Cardinal and ordinal arithmetics of $n$ -ary relational systems and $n$ -ary ordered sets

Jiří Karásek (1998)

Mathematica Bohemica

The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for $n$ -ary relational systems. $n$ -ary ordered sets are defined as special $n$ -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of $n = 2$ or 3. The class of $n$ -ary ordered sets is then closed under the cardinal and ordinal operations.

Cardinal arithmetic of a certain class of monounary algebras

Jiří Novotný (1986)

Časopis pro pěstování matematiky

Cardinal arithmetic of general relational systems

Josef Šlapal (1993)

Czechoslovak Mathematical Journal

Cardinal multiplication of structures with a reflexive relation

Ralph McKenzie (1971)

Fundamenta Mathematicae

Cardinalities of lattices of topologies of unars and some related topics

Anna Kartashova (2001)

Discussiones Mathematicae - General Algebra and Applications

In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.

Cardinality of retracts of monounary algebras

Danica Jakubíková-Studenovská, Jozef Pócs (2008)

Czechoslovak Mathematical Journal

For an uncountable monounary algebra $(A, f)$ with cardinality $κ$ it is proved that $(A, f)$ has exactly $2^{κ}$ retracts. The case when $(A, f)$ is countable is also dealt with.

Cartesian closedness in categories of partial algebras.

Šlapal, Josef (1996)

Mathematica Pannonica

Categories of functors between categories with partial morphisms

Hans-Jürgen Vogel (2005)

Discussiones Mathematicae - General Algebra and Applications

It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.

Categories of locally diagonal partial algebras.

Šlapal, Josef (2004)

Beiträge zur Algebra und Geometrie

Categories of systems of $X$ -relations

Jiří Rachůnek (1980)

Archivum Mathematicum

Category of commutative groupoids is binding

Jiří Sichler (1967)

Commentationes Mathematicae Universitatis Carolinae

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.

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